Orientadores: Luiz Antonio Barrera San Martin, Osvaldo Germano do Rocio / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-08T09:10:31Z (GMT). No. of bitstreams: 1 Verdi_MarcosAndre_D.pdf: 586732 bytes, checksum: c0182ba0a69107acd3d5548e682641df (MD5) Previous issue date: 2007 / Resumo:Neste trabalho estudamos dois problemas distintos: ações de semigrupos em órbitas adjuntas e compactificações de semigrupos. Quanto ao estudo das ações de semigrupos, consideramos um grupo de Lie semi-simples, não compacto, conexo e com centro finito G e a órbita adjunta de G através de elementos H pertencentes a uma subalgebra abeliana maximal contida na parte não-compacta de uma decomposição de Cartan de G. Tomamos então um semigrupo S Ì G com pontos interiores e descrevemos os conjuntos de controle para a ação de S nestas órbitas. Mostramos também que esses conjuntos não são comparáveis utilizando a relação de ordem usual para conjuntos de controle e descrevemos seus domínios de atração. Consideramos também o caso em que S é um semigrupo maximal, obtendo uma descrição melhor dos conjuntos de controle. Para compactificações de semigrupos, adotamos as mesmas hipóteses sobre G e tomamos S como o semigrupo de compressão de um subconjunto fechado da variedade ??ag?maximal de G. Obtemos uma compactificação do espaço homogêneo G/H, onde H denota o grupo das unidades de S, como um subconjunto dos conjuntos fechados de G e mostramos que quando G tem posto 1 é possível realizar a imagem de S/H por essa compactificações no conjunto dos subconjuntos fechados da variedade flag maximal de G / Abstract: In this work we study two distinct problems: semigroup actions on adjoint orbits and compactication of semigroups. For the study of the semigroup actions, we consider a semi-simple connected noncompact Lie group G and the adjoint orbit through elements in a maximal abelian subalgebra contained in the complement of a maximal compactly embedded subalgebra of the Lie algebra of G. We take then a semigroup S Ì G with interior points and describe the control sets for the S-action on these orbits. It is proved here that these control sets are no comparable and we describe its domains of attraction. We also consider the case in that S is a maximal semigroup and obtain a better description of the control sets. For the compactication of semigroups, we use the same hypothesis about G and consider S as the compression semigroup of a closed subset in the maximal ag manifold of G. We obtain a compactication of the homogeneous space G/H, where H=S ÇS-1, as a subset of the set of closed sets of G and we show that when G has rank one is possible to realize the image of S/H under this compacti?cation in the set of the closed subsets of the maximal ag manifold / Doutorado / Doutor em Matemática

Spaces such as the closed interval [0, 1] do not have the property of being homogeneous, strongly locally homogeneous (SLH) or countable dense homogeneous (CDH), but the Hilbert cube has all three properties. We investigate subsets X of real numbers to determine when their countable product is homogeneous, SLH, or CDH. We give necessary and sufficient conditions for the product to be homogeneous. We also prove that the product is SLH if and only if X is zero-dimensional or an interval. And finally we show that for a Borel subset X of real numbers the product is CDH iff X is a G-delta zero-dimensional set or an interval.

No description available.

In this thesis, we study the Ricci flow and Ricci soliton equations on Riemannian manifolds which admit a certain degree of symmetry. More precisely, we investigate the Ricci soliton equation on connected Riemannian manifolds, which carry a cohomogeneity one action by a compact Lie group of isometries, and the Ricci flow equation for invariant metrics on a certain class of compact and connected homogeneous spaces. In the first case, we prove that the initial value problem for a cohomogeneity one gradient Ricci soliton around a singular orbit of the group action always has a solution, under a technical assumption. However, this solution is in general not unique. This is a generalisation of the analogous result for the Einstein equation, which was proved by Eschenburg and Wang in their paper "Initial value problem for cohomogeneity one Einstein metrics". In the second case, by studying the corresponding system of nonlinear ODEs, we identify a class of singular behaviours for the homogeneous Ricci flow on these spaces. The singular behaviours that we find all correspond to type I singularities, which are modelled on rigid shrinking solitons. In the case where the isotropy representation decomposes into two invariant irreducible inequivalent summands, we also investigate the existence of ancient solutions and relate this to the existence and non existence of invariant Einstein metrics. Furthermore, in this special case, we also allow the initial metric to be pseudo- Riemannian and we investigate the existence of immortal solutions. Finally, we study the behaviour of the scalar curvature for this more general situation and show that in the Riemannian case it always has to turn positive in finite time, if it was negative initially. By contrast, in the pseudo-Riemannian case, there are certain initial conditions which preserve negativity of the scalar curvature.

Within Spanish cultural studies, urban studies have become increasingly popular in the last twenty years. While this literature covers a wide range of Spanish locales and historical periods, there are still few comprehensive analyses of the production of Madrid's urban space between the Civil War and the economic boom of the 1960s. This dissertation contributes to the field through the examination of the symbolic production and use of Madrid during the first decades of the Franco dictatorship. I argue that the disciplining of Madrid's urban space was a means of organizing the capital's citizens into ordered subjects during a time of transition. This process was carried out primarily through the creation of expectations of how the spaces around the urban subject were best lived. My analytical approach is based on case studies and close readings of films, novels, and official documents such as speeches, maps, laws, and urban policies that were produced during the 1940s and 50s. It is an interdisciplinary study of the disciplining of Madrid and its inhabitants. The dissertation is organized spatially; each chapter focuses on a different aspect of Madrid's urban fabric, which extends outward in a series of concentric circles. My first chapter, "Home Life: Domestic Struggles in Comedic Film," deals with the most intimate human space, the home. Four films, Esa pareja feliz (dir. Juan Antonio Bardem and Luis García Berlanga, 1951), El inquilino (dir. José Antonio Nieves Conde, 1957), La vida por delante (dir. Fernando Fernán Gómez, 1958), and El pisito (dir. Marco Ferreri, 1959) illustrate how pressures of ownership transformed the home into a powerful tool of control and homogenization by blurring the lines between public and private space. In Chapter 2, "A Wandering Man: Fragmentation and Discipline in La colmena," I show that this tension spread to the city streets portrayed in Camilo José Cela's novel (1951), where fragmentation and separation worked to break down the threat of collective action and caused individuals to search for a productive role in society. In the 1950s, the push of hunger and the pull of industrialization drew migrants to Madrid in search of jobs and material comforts, only to find themselves displaced to the periphery of the capital, reinforcing their marginal status. This demographic transformation forms the basis for my third chapter, "No Limits! The City in Surcos and Los golfos," in which I analyze two key films from the decade, José Antonio Nieves Conde's Surcos (1951) and Carlos Saura's Los golfos (1959). Finally, Chapter Four, "'Ya se aburren de tanta capital': Leisure, Language, and Law in El Jarama" examines Rafael Sánchez Ferlosio's novel (1956) to explore how citizens looking for relief from the pressures of city life in the surrounding countryside only found that this leisure space was under the control of its own disciplinary forces. The novels and films that I include in this study demonstrate how the discipline of the Spanish capital extended to all of the city's zones to create a model of urban citizenship that blurred the lines between pubic and private space and between individual and collective subjects.

This thesis is concerned with the formulation of a suitable notion of monotonicity of discrete and continuous-time dynamical systems on Lie groups and homogeneous spaces. In a linear space, monotonicity refers to the property of a system that preserves an ordering of the elements of the space. Monotone systems have been studied in detail and are of great interest for their numerous applications, as well as their close connections to many physical and biological systems. In a linear space, a powerful local characterisation of monotonicity is provided by differential positivity with respect to a constant cone field, which combines positivity theory with a local analysis of nonlinear systems. Since many dynamical systems are naturally defined on nonlinear spaces, it is important to seek a suitable adaptation of monotonicity on such spaces. However, the question of how one can develop a suitable notion of monotonicity on a nonlinear manifold is complicated by the general absence of a clear and well-defined notion of order on such a space. Fortunately, for Lie groups and important examples of homogeneous spaces that are ubiquitous in many problems of engineering and applied mathematics, symmetry provides a way forward. Specifically, the existence of a notion of geometric invariance on such spaces allows for the generation of invariant cone fields, which in turn induce notions of conal orders. We propose differential positivity with respect to invariant cone fields as a natural and powerful generalisation of monotonicity to nonlinear spaces and develop the theory in this thesis. We illustrate the ideas with numerous examples and apply the theory to a number of areas, including the theory of consensus on Lie groups and order theory on the set of positive definite matrices.

Orientador: Luiz Antonio Barrera San Martin / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-10T08:58:03Z (GMT). No. of bitstreams: 1 Ferraiol_ThiagoFanelli_M.pdf: 1209828 bytes, checksum: 5848b00f7a22bffd43d384f4102b061d (MD5) Previous issue date: 2008 / Resumo: Nesta dissertacao apresentamos os conceitos fundamentais de entropia em sistemas dinamicos e algumas relacoes entre entropia metrica e topologica. O objetivo principal e calcular a entropia de algumas transformacoes em espacos homogeneos induzidas por acoes de Grupos de Lie. Para analizar, mostramos que a entropia de translações em variedades fag e sempre zero / Abstract: On this dissertation we present the fundamentals concepts of entropy in dynamical systems and some relations among metric and topological entropy. The main goal is calculate the entropy of some transformations on homogeneous spaces induced by Lie groups actions. About to analize, we show that the entropy of translations on flag manifolds is always zero / Mestrado / Mestre em Matemática

Orientadores: Francesco Mercuri, Stefano Montaldo / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-04T19:19:12Z (GMT). No. of bitstreams: 1 Onnis_IreneIgnazia_D.pdf: 2069054 bytes, checksum: 1e17d831ed9d0ddf66676ec47d7161f4 (MD5) Previous issue date: 2005 / Resumo: Neste trabalho estudamos superfícies em variedades Riemannianas homogêneas tridimensionais com condições sobre a geometria intrínseca e/ou extrínseca. Em particular: 1. Resolvemos o Problema de Bjõrling para superfícies mínimas que contêm uma dada faixa analítica em grupos de Lie munidos de uma métrica invariante à esquerda. 2. Classificamos as superfícies de curvatura média constante no produto do plano hiperbólico com a reta real, que são invariantes pela ação de um subgrupo a umparâmetro do grupo das isometrias do espaço ambiente. 3. Classificamos as superfícies de curvatura Gaussiana constante em variedades Riemannianas homogêneas de dimensão três, com particular atenção ao caso do grupo de Heisenberg e do espaço dado pelo produto do plano hiperbólico com a reta real / Abstract: In this work we study surfaces in homogeneous Riemannian manifolds of dimension three with conditions on the intrinsic and/or the extrinsic geometry. En particular: 1. We solve the Bjõrling Problem for minimal surfaces which contain an analytical strip in Lie groups with a left invariant metric. 2. We classify constant mean curvature surfaces in the product of the hyperbolic plane with the realline, which are invariant under the action of a one-parameter subgroup of the isometries group of the ambient space. 3. We classify constant Gaussian curvature surfaces of homogeneous Riemannian manifolds of dimension three, with particular attention for the case of the Heisenberg group and for the product of the hyperbolic plane and the realline / Doutorado / Geometria Diferencial / Doutor em Matemática

No description available.

Orientador: Sueli Irene Rodrigues Costa / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-09-11T21:20:45Z (GMT). No. of bitstreams: 1 Bressan_JoaoPaulo_D.pdf: 1164660 bytes, checksum: 4825edafe6fbea5e3bc43934bc528376 (MD5) Previous issue date: 2012 / Resumo: A partir das desigualdades de Hamming e Gilbert-Varshamov obtém-se um limitante superior e um limitante inferior para o número de pontos de um código numa variedade flag geométrica. Isto é feito tomando-se uma estimativa para o volume de bolas geodésicas, que resulta de cálculos envolvendo a curvatura seccional destas variedades. Em particular, são derivados limitantes para empacotamentos de esferas numa variedade de Grassmann complexa. Um limitante superior para a distância mínima também é obtido através da inversa da função que calcula o volume de um chapéu esférico. Esta técnica geométrica também é aplicada no estudo de limitantes para empacotamentos em alguns casos particulares de variedades flag maximais. Através de procedimentos computacionais, tais limitantes são implementados numericamente em alguns exemplos. Uma motivação para este trabalho foi à busca de possíveis extensões de alguns resultados sobre as grassmanianas complexas, cujo interesse na área de comunicações vem de uma interpretação que pode ser feita da transmissão em canais MIMO não coerentes via códigos em tais variedades / Abstract: Upper and lower bounds for the number of points of codes in geometric flag manifolds are obtained from Hamming and Gilbert-Varshamov inequalities. This is done by taking an estimate for the volume of geodesic balls, as a result of calculations involving the sectional curvature of such manifolds. As a particular case, sphere packing bounds in complex Grassmann manifolds are derived. An upper bound on the minimum distance is also obtained through the inverse mapping for the volume of spherical caps. This geometric technique is also applied in the study of sphere packing bounds in some particular cases of full-flag manifolds. Such bounds are numerically implemented in some examples. One motivation for this work was the search for possible extensions of some results on complex Grassmann manifolds, which interest in communications comes from a model for the transmition on non-coherent MIMO channels via codes in such manifolds / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada