The use of Hilbert space theory became an important tool for ergodic theoreticians ever since John von Neumann proved the fundamental Mean Ergodic theorem in Hilbert space. Recurrence is one of the corner stones in the study of dynamical systems. In this dissertation some extended ideas besides those of the basic, well-known recurrence results are investigated. Hilbert space theory proves to be a very useful approach towards the solution of multiple recurrence problems in ergodic theory. Another very important use of Hilbert space theory became evident only relatively recently, when it was realized that non-commutative dynamical systems become accessible to the ergodic theorist through the important Gelfand-Naimark-Segal (GNS) representation of C*-algebras as Hilbert spaces. Through this construction we are enabled to invoke the rich catalogue of Hilbert space ergodic results to approach the more general, and usually more involved, non-commutative extensions of classical ergodic-theoretical results. In order to make this text self-contained, the basic, standard, ergodic-theoretical results are included in this text. In many instances Hilbert space counterparts of these basic results are also stated and proved. Chapters 1 and 2 are devoted to the introduction of these basic ergodic-theoretical results such as an introduction to the idea of measure-theoretic dynamical systems, citing some basic examples, Poincairé’s recurrence, the ergodic theorems of Von Neumann and Birkhoff, ergodicity, mixing and weakly mixing. In Chapter 2 several rudimentary results, which are the basic tools used in proofs, are also given. In Chapter 3 we show how a Hilbert space result, i.e. a variant of a result by Van der Corput for uniformly distributed sequences modulo 1, is used to simplify the proofs of some multiple recurrence problems. First we use it to simplify and clarify the proof of a multiple recurrence result by Furstenberg, and also to extend that result to a more general case, using the same Van der Corput lemma. This may be considered the main result of this thesis, since it supplies an original proof of this result. The Van der Corput lemma helps to simplify many of the tedious terms that are found in Furstenberg’s proof. In Chapter 4 we list and discuss a few important results where classical (commutative) ergodic results were extended to the non-commutative case. As stated before, these extensions are mainly due to the accessibility of Hilbert space theory through the GNS construction. The main result in this section is a result proved by Niculescu, Ströh and Zsidó, which is proved here using a similar Van der Corput lemma as in the commutative case. Although we prove a special case of the theorem by Niculescu, Ströh and Zsidó, the same method (Van der Corput) can be used to prove the generalized result. Copyright 2004, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. Please cite as follows: Beters, FJC 2004, A Hilbert space approach to multiple recurrence in ergodic theory, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd-02222006-104936 / > / Dissertation (MSc (Applied Mathematics))--University of Pretoria, 2007. / Mathematics and Applied Mathematics / unrestricted

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: This work employs perturbation techniques to price and hedge financial derivatives in a stochastic volatility framework. Fouque et al. [44] model volatility as a function of two processes operating on different time-scales. One process is responsible for the fast-fluctuating feature of volatility and corresponds to the slow time-scale and the second is for slowfluctuations or fast time-scale. The former is an Ergodic Markov process and the latter is a strong solution to a Lipschitz stochastic differential equation. This work mainly involves modelling, analysis and estimation techniques, exploiting the concept of mean reversion of volatility. The approach used is robust in the sense that it does not assume a specific volatility model. Using singular and regular perturbation techniques on the resulting PDE a first-order price correction to Black-Scholes option pricing model is derived. Vital groupings of market parameters are identified and their estimation from market data is extremely efficient and stable. The implied volatility is expressed as a linear (affine) function of log-moneyness-tomaturity ratio, and can be easily calibrated by estimating the grouped market parameters from the observed implied volatility surface. Importantly, the same grouped parameters can be used to price other complex derivatives beyond the European and American options, which include Barrier, Asian, Basket and Forward options. However, this semi-analytic perturbative approach is effective for longer maturities and unstable when pricing is done close to maturity. As a result a more accurate technique, the decomposition pricing approach that gives explicit analytic first- and second-order pricing and implied volatility formulae is discussed as one of the current alternatives. Here, the method is only employed for European options but an extension to other options could be an idea for further research. The only requirements for this method are integrability and regularity of the stochastic volatility process. Corrections to [3] remarkable work are discussed here. / AFRIKAANSE OPSOMMING: Hierdie werk gebruik steuringstegnieke om finansiële afgeleide instrumente in ’n stogastiese wisselvalligheid raamwerk te prys en te verskans. Fouque et al. [44] gemodelleer wisselvalligheid as ’n funksie van twee prosesse wat op verskillende tyd-skale werk. Een proses is verantwoordelik vir die vinnig-wisselende eienskap van die wisselvalligheid en stem ooreen met die stadiger tyd-skaal en die tweede is vir stadig-wisselende fluktuasies of ’n vinniger tyd-skaal. Die voormalige is ’n Ergodiese-Markov-proses en die laasgenoemde is ’n sterk oplossing vir ’n Lipschitz stogastiese differensiaalvergelyking. Hierdie werk behels hoofsaaklik modellering, analise en skattingstegnieke, wat die konsep van terugkeer to die gemiddelde van die wisseling gebruik. Die benadering wat gebruik word is rubuust in die sin dat dit nie ’n aanname van ’n spesifieke wisselvalligheid model maak nie. Deur singulêre en reëlmatige steuringstegnieke te gebruik op die PDV kan ’n eerste-orde pryskorreksie aan die Black-Scholes opsie-waardasiemodel afgelei word. Belangrike groeperings van mark parameters is geïdentifiseer en hul geskatte waardes van mark data is uiters doeltreffend en stabiel. Die geïmpliseerde onbestendigheid word uitgedruk as ’n lineêre (affiene) funksie van die log-geldkarakter-tot-verval verhouding, en kan maklik gekalibreer word deur gegroepeerde mark parameters te beraam van die waargenome geïmpliseerde wisselvalligheids vlak. Wat belangrik is, is dat dieselfde gegroepeerde parameters gebruik kan word om ander komplekse afgeleide instrumente buite die Europese en Amerikaanse opsies te prys, dié sluit in Barrier, Asiatiese, Basket en Stuur opsies. Hierdie semi-analitiese steurings benadering is effektief vir langer termyne en onstabiel wanneer pryse naby aan die vervaldatum beraam word. As gevolg hiervan is ’n meer akkurate tegniek, die ontbinding prys benadering wat eksplisiete analitiese eerste- en tweede-orde pryse en geïmpliseerde wisselvalligheid formules gee as een van die huidige alternatiewe bespreek. Hier word slegs die metode vir Europese opsies gebruik, maar ’n uitbreiding na ander opsies kan’n idee vir verdere navorsing wees. Die enigste vereistes vir hierdie metode is integreerbaarheid en reëlmatigheid van die stogastiese wisselvalligheid proses. Korreksies tot [3] se noemenswaardige werk word ook hier bespreek.

Cette thèse est consacrée à l'étude des différents problèmes liés aux structures des cubes , en théorie ergodique et en dynamique topologique. Elle est composée de six chapitres. La présentation générale nous permet de présenter certains résultats généraux en théorie ergodique et dynamique topologique. Ces résultats, qui sont associés d'une certaine façon aux structures des cubes, sont la motivation principale de cette thèse. Nous commençons par les structures de cube introduites en théorie ergodique par Host et Kra (2005) pour prouver la convergence dans $L^2 $ de moyennes ergodiques multiples. Ensuite, nous présentons la notion correspondante en dynamique topologique. Cette théorie, développée par Host, Kra et Maass (2010), offre des outils pour comprendre la structure topologique des systèmes dynamiques topologiques. En dernier lieu, nous présentons les principales implications et extensions dérivées de l'étude de ces structures. Ceci nous permet de motiver les nouveaux objets introduits dans la présente thèse, afin d'expliquer l'objet de notre contribution. Dans le Chapitre 1, nous nous attachons au contexte général en théorie ergodique et dynamique topologique, en mettant l'accent sur l'étude de certains facteurs spéciaux. Les Chapitres 2, 3, 4 et 5 nous permettent de développer les contributions de cette thèse. Chaque chapitre est consacré à un thème particulier et aux questions qui s'y rapportent, en théorie ergodique ou en dynamique topologique, et est associé à un article scientifique. Les structures de cube mentionnées plus haut sont toutes définies pour un espace muni d'une unique transformation. Dans le Chapitre 2, nous introduisons une nouvelle structure de cube liée à l'action de deux transformations S et T qui commutent sur un espace métrique compact X. Nous étudions les propriétés topologiques et dynamiques de cette structure et nous l'utilisons pour caractériser les systèmes qui sont des produits ou des facteurs de produits. Nous présentons également plusieurs applications, comme la construction des facteurs spéciaux. Le Chapitre 3 utilise la nouvelle structure de cube définie dans le Chapitre 2 dans une question de théorie ergodique mesurée. Nous montrons la convergence ponctuelle d'une moyenne cubique dans un système muni deux transformations qui commutent. Dans le Chapitre 4, nous étudions le semigroupe enveloppant d'une classe très importante des systèmes dynamiques, les nilsystèmes. Nous utilisons les structures des cubes pour montrer des liens entre propriétés algébriques du semigroupe enveloppant et les propriétés topologiques et dynamiques du système. En particulier, nous caractérisons les nilsystèmes d'ordre 2 par une propriété portant sur leur semigroupe enveloppant. Dans le Chapitre 5, nous étudions les groupes d'automorphismes des espaces symboliques unidimensionnels et bidimensionnels. Nous considérons en premier lieu des systèmes symboliques de faible complexité et utilisons des facteurs spéciaux, dont certains liés aux structures de cube, pour étudier le groupe de leurs automorphismes. Notre résultat principal indique que, pour un système minimal de complexité sous-linéaire, le groupe d'automorphismes est engendré par l'action du shift et un ensemble fini. Par ailleurs, en utilisant les facteurs associés aux structures de cube introduites dans le Chapitre 2, nous étudions le groupe d'automorphismes d'un système de pavages représentatif. La bibliographie, commune à l'ensemble de la thèse, se trouve en fin document / This thesis is devoted to the study of different problems in ergodic theory and topological dynamics related to og cube structures fg. It consists of six chapters. In the General Presentation we review some general results in ergodic theory and topological dynamics associated in some way to cubes structures which motivates this thesis. We start by the cube structures introduced in ergodic theory by Host and Kra (2005) to prove the convergence in $L^2$ of multiple ergodic averages. Then we present its extension to topological dynamics developed by Host, Kra and Maass (2010), which gives tools to understand the topological structure of topological dynamical systems. Finally we present the main implications and extensions derived of studying these structures, we motivate the new objects introduced in the thesis and sketch out our contributions. In Chapter 1 we give a general background in ergodic theory and topological dynamics given emphasis to the treatment of special factors. % We give basic definitions and describe special factors associated to a From Chapter 2 to Chapter 5 we develop the contributions of this thesis. Each one is devoted to a different topic and related questions, both in ergodic theory and topological dynamics. Each one is associated to a scientific article. In Chapter 2 we introduce a novel cube structure to study the actions of two commuting transformations $S$ and $T$ on a compact metric space $X$. In the same chapter we study the topological and dynamical properties of such structure and we use it to characterize products systems and their factors. We also provide some applications, like the construction of special factors. In the same topic, in Chapter 3 we use the new cube structure to prove the pointwise convergence of a cubic average in a system with two commuting transformations. In Chapter 4, we study the enveloping semigroup of a very important class of dynamical systems, the nilsystems. We use cube structures to show connexions between algebraic properties of the enveloping semigroup and the geometry and dynamics of the system. In particular, we characterize nilsystems of order 2 by its enveloping semigroup. In Chapter 5 we study automorphism groups of one-dimensional and two-dimensional symbolic spaces. First, we consider low complexity symbolic systems and use special factors, some related to the introduced cube structures, to study the group of automorphisms. Our main result states that for minimal systems with sublinear complexity such groups are spanned by the shift action and a finite set. Also, using factors associated to the cube structures introduced in Chapter 2 we study the automorphism group of a representative tiling system. The bibliography is defer to the end of this document

This thesis contributes to two completely unrelated debates in the economic literature, similar only in the relatively high degree of controversy characterizing each one. The first part is methodological and macroeconomic in nature, addressing the question of whether the distribution of income across countries is converging (i.e. are the poor catching up to the rich?) or diverging (i.e. are we witnessing the formation of two exclusive clubs, one for poor countries and another one for rich countries?). Applications of the simple Markov model to this question have generated evidence in favor of the divergence hypothesis. In the first chapter, I critically review these results. I use statistical inference to show that the divergence results are not statistically robust, and I explain that this instability of the results comes from the application of a model for discrete data to data that is actually continuous. In the second chapter, I reposition the whole convergence-divergence debate by placing it in the context of Silverman’s classic survey of non-parametric density estimation techniques. This allows me to use the basic notions of fuzzy logic to adapt the simple Markov chain model to continuous data. When I apply the newly adapted Markov chain model to the cross-country distribution question, I find evidence against the divergence hypothesis, and this evidence is statistically robust. The second part of the thesis is empirical and microeconomic in nature. I question whether observed differences between husbands’ and wives’ participation in labor markets are due to different preferences or to different constraints. My identification strategy is based on the idea that the more power an individual has relative to his/her partner, the more his/her actions will reflect his/her preferences. I use 2001 PSID data on cohabiting couples to estimate a simultaneous equations model of the spousal time allocation decision. My results confirm the stylized fact that specialization and trade does not explain time allocation for couples in which the wife is the primary breadwinner, and suggest that power could provide a more general explanation of the observations. My results show that wives with relatively more power choose to work more on the labor market and less at home, whereas husbands with more power choose to do the opposite. Since women start out from a lower level of labor market participation than men do, it would seem that spouses’ agree that the ideal mix of market work and housework lies somewhere between the husbands’ and the wives’ current positions.

This thesis discusses three distinct topics. A topological space X is said to be self- Tietze if for every closed C eX, every continuous f: C -+ X admits a continuous extension F: X -+ X. We show that every disconnected, self- Tietze space is ultranormal. The Tychonoff Plank is an example of a compact self- Tietze space which is not completely normal, and we establish that a completely normal, zero- dimensional, homogeneous space need not be self- Tietze. A subset of the plane is a two-point set if it meets every straight line in exactly two points. We show that a two-point set cannot contain a dense G8 subset of an arc. We also show that the complement of a two-point set is necessarily path-connected. Finally, we construct a zero-dimensional subset of the plane of which the complement is simply-connected. For A E lR, the tent-map with slope A is the function f: [0, 1] -+ lR such that f(x) = AX for x :=:; ~ and f(x) = A(l - x) for x ~ ~. Properties of w-limit sets of tent-maps, i.e. sets of the form n {fn+k(x) I kEN} nEN for x E [0,1], are examined, and an example of a tent-map and a closed, invariant, nonempty, internally chain transitive subset of [0, 1] which is not an w-limit set is given.

Ce travail étudie les déviations de sommes ergodiques pour des systèmes dynamiques substitutifs avec une matrice qui admet des valeurs propres de module supérieur à 1. Précisément, nous nous concentrons sur les substitutions telle que ces valeurs propres ne sont pas conjuguées. Dans un premier temps, on défini les lettres a-minimales et dominantes d'un mot pour étudier sa ligne brisée associé. On défini la ligne brisée normalisée et sa fonction limite. Pour l'étude des sommes ergodiques, on défini le sous-automate des lettres minimales. On donne des conditions sur une substitution de sorte qu'il y ait un nombre infini des sommes ergodiques égales à zéro pour un point x 2 X. Enfin, en utilisant un boucle dans une classe de Rauzy, on prouve l'existence d'un nombre infini d'échanges d'intervalles auto-similaires, dont la matrice de Rauzy a deux valeurs propres non conjuguées de module supérieur à 1. Et tout échange d'intervalles affine semi-conjugué à cet échange d'intervalles est aussi conjugué. / This thesis focuses on the deviation of ergodic sums for a substitution dynamical systems with a matrix that admits eigenvalues of modulus larger than 1. Specifically, we concentrate on substitutions with non-conjugated eigenvalues. At first, we define the a-minimals letters and the dominant letters of a word to study its broken associated line. We define the normalize broken line and its limit function. For the study of ergodic sums, we define the sub-automaton of minimum letters. We give conditions on a substitution so that there is infinitely many zero sums ergodic for a point x 2 X. Finally, using a loop in a class of Rauzy, we prove the existence of infinitely many interval exchange transformation self-similar, whose Rauzy matrix has two non-conjugated eigenvalues larger than 1 and every affine interval exchange transformation that is semi-conjugated, is also conjugated.

Walking in the house of Daedalus – An analysis of the katabasis motif in Mark Z. Danielewski’s House of Leaves   This study analyses the depiction of the labyrinth as a symbolic landscape in regard to both subject and form in the multi-layered novel House of Leaves by Mark Z. Danielewski. Using the mythological katabasis motif as a structural principle, this study discusses modern labyrinthine narratives wherein selfhood is constructed through an infernal journey between a descent and a return. This study analyses the novel with a thematic perspective from two points of view; how the labyrinth acts as central motif for the self in the novel and how the novel visually depicts the narrative through typographical choices throughout the text. The study’s main question is how the novel depicts the labyrinth in regard to its historical and cultural context and how it inscribes itself into a tradition of narratives that depicts the labyrinth as a metaphor for the mind and as a symbol for the exploration of the self.   The result shows that House of Leaves uses a complex cluster of narratives to tell a katabatic story, both through the narrative and the form. Through the symbolic landscape and through the use of a genre typical and uncanny horror story, House of Leaves tells a story about alienation, guilt and love where the characters psychological developments changes in regard to confrontations with the labyrinth and through the symbolical tests that exists throughout the katabatic journey. The characters ascends traumatized from the labyrinth, but are at the same time rewarded with personal insight

How one behaves after interacting with a friend may not be the same as before the interaction began What factors a ect the formation of social interactions between people and, once formed, how do social interactions leave lasting changes on individual behavior? In this dissertation, a thorough review and conceptual synthesis is provided Major features of coordination dynamics are demonstrated with examples from both the intrapersonal and interpersonal coordination literature that are interpreted via a conceptual scheme, the causal loops of coordination dynamics An empirical, behavioral study of interpersonal coordination was conducted to determine which spontaneous patterns of coordination formed and whether a remnant of the interaction ensued ("social memory") To assess social memory in dyads, the behavior preceding and following episodes of interaction was compared In the experiment, pairs of people sat facing one another and made continuous flexion-extension finger movements while a window acted as a shutter to control whether partners saw each other's movements Thus, vision ("social contact") allowed spontaneous information exchange between partners through observation Each trial consisted of three successive intervals lasting twenty seconds: without social contact ("me and you"), with social contact ("us"), and again without ("me and you") During social contact, a variety of patterns was observed ranging from phase coupling to transient or absent collective behavior Individuals also entered and exited social coordination differently In support of social memory, compared to before social contact, after contact ended participants tended to remain near each other's movement frequency Furthermore, the greater the stability of coupling, the more similar the partners' post-interactional frequencies were Proposing that the persistence of behavior in the absence of information exchange was the result of prior frequency adaptation, a mathematical model of human movement was implemented with Haken-Kelso-Bunz oscillators that reproduced the experimental findings, even individual dyadic patterns Parametric manipulations revealed multiple routes to persistence of behavior via the interplay of adaptation and other HKB model parameters The experimental results, the model, and their interpretation form the basis of a proposal for future research and possible therapeutic applications / Includes bibliography / Dissertation (PhD)--Florida Atlantic University, 2016 / FAU Electronic Theses and Dissertations Collection

Este trabalho estuda as características textuais dos chamados role playing games \'pedagógicos\', com uma dupla finalidade: explicitar alguns dos aspectos que distinguem o jogo de aventura enquanto um tipo de texto, e refletir sobre sua utilização como instrumento pedagógico. O corpus é constituído por dois jogos de aventura com finalidade pedagógica, veiculados em dois suportes: um encarte e um livro. O encarte-jogo integra a Revista do Ensino Médio do MEC (2004) e traz um jogo de aventura bastante simplificado, A travessia do Liso do Suçuarão, baseado no romance Grande Sertão: veredas, de Guimarães Rosa. O livro-jogo traz uma aventura mais complexa que versa sobre o roubo de uma tela de Portinari, O resgate de \"Retirantes\", e faz parte da série Mini-Gurps, desenvolvida para jogadores iniciantes, publicada pela Editora Devir (SP). O quadro teórico que orienta a pesquisa está centrado, principalmente, em aportes da teoria ergódica da literatura, proposta por Aarseth (1997) e, quando necessário e pertinente, foram consideradas também as contribuições de outros teóricos do texto e do discurso, particularmente, os trabalhos de Koch (2002; 2003; 2005) e Maingueneau (1996; 1997; 2001; 2002; 2004). Os jogos de aventura selecionados foram analisados em duas etapas: uma de leitura e outra de observação de uma partida sobre um desses jogos. Na etapa de leitura, o analista coloca-se como operador do texto do jogo com o objetivo de aprendê-lo, explicitando as características hipertextuais desse tipo de texto e as habilidades de leitura que ele requer. Na etapa de observação de uma partida do livro-jogo O resgate de \"Retirantes\", o analista desvela, a partir da ação do Mestre e de sua interação com o grupo de jogadores, a atualização de uma versão possível dessa aventura: proximidade ou distanciamento em relação à aventura proposta no livro-jogo. A explicitação de algumas das características ergódicas desses dois jogos de aventura levam a rediscutir o componente pedagógico que se vem associando a eles. A finalidade pedagógica dos jogos não está centrada no conteúdo informacional que o texto de ficção ajudaria a transmitir, mas sim nas habilidades de leitura e de representação dos jogos. / This paper studies the textual characteristics of the so-called pedagogical role-playing games, with a dual purpose: to explain some of the aspects that distinguish the adventure game as a kind of text and to reflect upon its usage as a pedagogical instrument. The corpus comprises two adventure games with pedagogical purposes, present in two means: an insert and a book. The insert-game is part of Revista do Ensino Médio do MEC (2004) and offers a very simplified adventure game, A travessia do Liso do Suçuarão, based on the novel Grande Sertão: veredas by Guimarães Rosa. The book-game delivers a more complex adventure that talks about the robbery of a Portinari canvas, O resgate de \"Retirantes\" and is part of the Mini-Gurps series, created for beginners, published by Editora Devir (SP). The theoretical frame that guides the research is mainly focused on contributions of the ergodic literary theory proposed by Aarseth (1997), and, whenever necessary and relevant, contributions from other text and discourse theorists were taken into account, especially the works by Koch (2002; 2003; 2005) and Maingueneau (1996; 1997; 2001; 2002; 2004). The selected adventure games underwent a two-step analysis: a reading stage, and one consisting of an observation of a session of one of these games. In the reading step, the analyst places herself as the game operator with the aim of learning it, exposing the hypertextual characteristics of this kind of text and the reading skills it requires. In the observation stage of a session of the book-game O resgate de \"Retirantes\", the analyst reveals, from the Master\'s action and his interaction with the group of players, the update of a possible version of this adventure: proximity or distance towards the adventure proposed in the book-game. Revealing some of the ergodic features of these two adventure games leads to discussing again the pedagogical component that has been associated to them. The pedagogical aim of the games is not centered on the informational content that the fiction text would help spread, but on the reading and representation skills of the games.

Este trabalho estuda as características textuais dos chamados role playing games \'pedagógicos\', com uma dupla finalidade: explicitar alguns dos aspectos que distinguem o jogo de aventura enquanto um tipo de texto, e refletir sobre sua utilização como instrumento pedagógico. O corpus é constituído por dois jogos de aventura com finalidade pedagógica, veiculados em dois suportes: um encarte e um livro. O encarte-jogo integra a Revista do Ensino Médio do MEC (2004) e traz um jogo de aventura bastante simplificado, A travessia do Liso do Suçuarão, baseado no romance Grande Sertão: veredas, de Guimarães Rosa. O livro-jogo traz uma aventura mais complexa que versa sobre o roubo de uma tela de Portinari, O resgate de \"Retirantes\", e faz parte da série Mini-Gurps, desenvolvida para jogadores iniciantes, publicada pela Editora Devir (SP). O quadro teórico que orienta a pesquisa está centrado, principalmente, em aportes da teoria ergódica da literatura, proposta por Aarseth (1997) e, quando necessário e pertinente, foram consideradas também as contribuições de outros teóricos do texto e do discurso, particularmente, os trabalhos de Koch (2002; 2003; 2005) e Maingueneau (1996; 1997; 2001; 2002; 2004). Os jogos de aventura selecionados foram analisados em duas etapas: uma de leitura e outra de observação de uma partida sobre um desses jogos. Na etapa de leitura, o analista coloca-se como operador do texto do jogo com o objetivo de aprendê-lo, explicitando as características hipertextuais desse tipo de texto e as habilidades de leitura que ele requer. Na etapa de observação de uma partida do livro-jogo O resgate de \"Retirantes\", o analista desvela, a partir da ação do Mestre e de sua interação com o grupo de jogadores, a atualização de uma versão possível dessa aventura: proximidade ou distanciamento em relação à aventura proposta no livro-jogo. A explicitação de algumas das características ergódicas desses dois jogos de aventura levam a rediscutir o componente pedagógico que se vem associando a eles. A finalidade pedagógica dos jogos não está centrada no conteúdo informacional que o texto de ficção ajudaria a transmitir, mas sim nas habilidades de leitura e de representação dos jogos. / This paper studies the textual characteristics of the so-called pedagogical role-playing games, with a dual purpose: to explain some of the aspects that distinguish the adventure game as a kind of text and to reflect upon its usage as a pedagogical instrument. The corpus comprises two adventure games with pedagogical purposes, present in two means: an insert and a book. The insert-game is part of Revista do Ensino Médio do MEC (2004) and offers a very simplified adventure game, A travessia do Liso do Suçuarão, based on the novel Grande Sertão: veredas by Guimarães Rosa. The book-game delivers a more complex adventure that talks about the robbery of a Portinari canvas, O resgate de \"Retirantes\" and is part of the Mini-Gurps series, created for beginners, published by Editora Devir (SP). The theoretical frame that guides the research is mainly focused on contributions of the ergodic literary theory proposed by Aarseth (1997), and, whenever necessary and relevant, contributions from other text and discourse theorists were taken into account, especially the works by Koch (2002; 2003; 2005) and Maingueneau (1996; 1997; 2001; 2002; 2004). The selected adventure games underwent a two-step analysis: a reading stage, and one consisting of an observation of a session of one of these games. In the reading step, the analyst places herself as the game operator with the aim of learning it, exposing the hypertextual characteristics of this kind of text and the reading skills it requires. In the observation stage of a session of the book-game O resgate de \"Retirantes\", the analyst reveals, from the Master\'s action and his interaction with the group of players, the update of a possible version of this adventure: proximity or distance towards the adventure proposed in the book-game. Revealing some of the ergodic features of these two adventure games leads to discussing again the pedagogical component that has been associated to them. The pedagogical aim of the games is not centered on the informational content that the fiction text would help spread, but on the reading and representation skills of the games.