Dans cette thèse, on s'intéresse aux systèmes dynamiques holomorphes dépendants de paramètres. Notre objectif est de contribuer à une théorie de la stabilité et des bifurcations en plusieurs variables complexes, généralisant celle des applications rationnelles fondées sur les travaux de Mané, Sad, Sullivan et Lyubich. Pour une famille d'applications d'allure polynomiale, on prouve l'équivalence de plusieurs notions de stabilité, entre autres une version asymptotique du mouvement holomorphe des cycles répulsifs et d'un sous-ensemble de l'ensemble de Julia de mesure pleine. Cela peut etre considéré comme une généralisation mesurable à plusieurs variables du célèbre lambda-lemme et nous permet de dégager un concept cohérent de stabilité dans ce cadre. Après avoir compris les bifurcations holomorphes, on s'intéresse à la continuité Hausdorff des ensembles de Julia. Nous relions cette propriété à l'existence de disques de Siegel dans l'ensemble de Julia, et donnons un exemple de ce phénomène. Finalement, on étudie la continuité du point de vue de l'implosion parabolique. Nous établissons un théorème de Lavaurs deux-dimensionel, ce qui nous permet d'étudier des phénomènes de discontinuité pour des perturbations d'applications tangentes à l'identité. / In this thesis we study holomorphic dynamical systems depending on parameters. Our main goal is to contribute to the establishment of a theory of stability and bifurcation in several complex variables, generalizing the one for rational maps based on the seminal works of Mané, Sad, Sullivan and Lyubich. For a family of polynomial like maps, we prove the equivalence of several notions of stability, among the others an asymptotic version of the holomorphic motion of the repelling cycles and of a full-measure subset of the Julia set. This can be seen as a measurable several variables generalization of the celebrated lambda-lemma and allows us to give a coherent definition of stability in this setting. Once holomorphic bifurcations are understood, we turn our attention to the Hausdorff continuity of Julia sets. We relate this property to the existence of Siegel discs in the Julia set, and give an example of such phenomenon. Finally, we approach the continuity from the point of view of parabolic implosion and we prove a two-dimensional Lavaurs Theorem, which allows us to study discontinuities for perturbations of maps tangent to the identity.

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-10-03T21:11:40Z No. of bitstreams: 2 Dissertação - Márcio Vaiz dos Reis - 2016.pdf: 2097960 bytes, checksum: 296b1790b8c8fe50c0e91d2d5ee204c4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-10-04T10:46:49Z (GMT) No. of bitstreams: 2 Dissertação - Márcio Vaiz dos Reis - 2016.pdf: 2097960 bytes, checksum: 296b1790b8c8fe50c0e91d2d5ee204c4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-10-04T10:46:49Z (GMT). No. of bitstreams: 2 Dissertação - Márcio Vaiz dos Reis - 2016.pdf: 2097960 bytes, checksum: 296b1790b8c8fe50c0e91d2d5ee204c4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-08-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The purpose of this dissertation is to present an introductory approach to the complex dynamics and fractal geometry, especially the Mandelbrot set. With the goal to simplify and stimulate the introduction of complex number in high school, the approach adopted was: the definition of the Mandelbrot set and its characteristics; the relationship between the Mandelbrot set and Julia set; how to find by using the Mandelbrot set. One of the tools used to help the teaching was Geogeobra, a dynamic software that allows the student to build the Mandelbrot set. Through this study, it is expected to motivate the learning of complex numbers by using fractal obtained by the study of function ( ) . Obtaining, as a result, a differentiated and motivating way of learning for a better understanding and intellectual development of the students. / Esse trabalho apresenta uma abordagem introdutória para a dinâmica complexa e a geometria fractal, em especial o conjunto de Mandelbrot. Com objetivo de facilitar e motivar a interação dos alunos com o ensino dos números complexos, a abordagem adotada foi: a definição do conjunto de Mandelbrot e suas características; a relação entre o conjunto de Mandelbrot e o conjunto de Julia; a relação do conjunto de Mandelbrot e o número . Uma das ferramentas utilizadas para auxiliar o professor foi o Geogeobra, um software dinâmico que permite o aluno a construção do conjunto de Mandelbrot. Por meio deste trabalho, espera-se motivar o ensino dos números complexos através do fractal obtido pelo estudo da função ( ) . Obtendo assim, como resultado, uma forma diferenciada e motivadora do aprendizado do aluno, garantindo um melhor entendimento e desenvolvimento intelectual.

Made available in DSpace on 2017-07-10T18:56:07Z (GMT). No. of bitstreams: 1 ELENI_TA.pdf: 6379839 bytes, checksum: ffb41203b6dc361310a2403cf7d37b74 (MD5) Previous issue date: 2016-08-18 / The research presented here focuses on reflections and analyses about woman‟s image according to the literary works of Julia Lopes de Almeida. It aimed at recalling woman‟s image from the nineteenth century in transition to the twentieth one, based on the following works: the brides‟ book (1896), Ladies and maidens‟ book (1906) and The intruder (1908). They were written by Julia Lopes de Almeida to understand the present‟s relationship with memory and past, consequently perceive that a new look can print new features to this story. This is a bibliographic research that is supported by authors who treat image, literature, history, memory and fiction, such as Benjamin (1989; 1994), Yates (2007), Ginzburg (1999, 2001), Assmann (2011), Guattari and Rolnik (1986), Needell (1993), Thompson (1998) Gagnebin (2005), Le Goff (1996), White (2001), Burke (1992), Halbwachs (1990) and Stallybrass (2008). This research also had access to the author's personal collection. As an investigation result, we can assure that Julia Lopes narratives provided elements to capture the different images of a woman, which are present on social life regarding the transition from the nineteenth to the twentieth century: a housewife, a bourgeois woman, a professional woman, a mother and devoted wife, as well as the woman in the convent. It was observed that there is not a single image of woman, but all women, somehow, are free to play her own role although, at the same time, they are trapped in social conventions. It concerns about a woman that has been idealized by the author from her experiences, in interaction of her subjectivities with singularities, and also asa social impersonation of the period / A pesquisa ora apresentada focalizou-se em reflexões e análises acerca da imagem da mulher nas obras de Julia Lopes de Almeida. Buscou-se rememorar a imagem da mulher do século XIX, na transição para o século XX, nas obras Livro das noivas (1896), Livro das donas e donzelas (1906) e A intrusa (1908), de Julia Lopes de Almeida, a fim de compreender a relação do presente com a memória e com o passado, entendendo que um novo olhar pode imprimir novos traços para essa história. Trata-se de uma pesquisa de cunho bibliográfico que se ancorou nos autores que tratam da imagem, literatura, história, memória e da ficção, tais como Benjamin (1989; 1994), Yates (2007), Ginzburg (1999; 2001), Assmann (2011), Guattari e Rolnik (1986), Needell (1993), Thompson (1998), Gagnebin (2005), Le Goff (1996), White (2001), Burke (1992), além de Halbwachs (1990) e Stallybrass (2008). A pesquisa contou também com o acesso ao acervo pessoal da autora. Como resultado de investigação, podemos afirmar que as narrativas de Julia Lopes forneceram elementos para captarmos as diversas imagens de mulher, presentes na vida social do século XIX na passagem para o século XX: a mulher dona de casa, a mulher burguesa, a mulher profissional, a mulher mãe e esposa dedicada, a mulher no convento. Foi possível perceber que não há uma única imagem de mulher, porém, todas as mulheres, de alguma forma, são livres para desempenhar cada qual o seu papel e, ao mesmo tempo, presas em convenções sociais. Trata-se de uma mulher apresentada pela autora a partir de suas experiências e vivências, na interação de suas subjetividades com as singularidades, também como uma representação social do período.

We generalize the notions of structural stability and hyperbolicity for the family of (multivalued) complex maps Hc(z) = zr + c; where r > 1 is rational and zr = exp r log z: We discovered that Hc is structurally stable at every hyperbolic parameter satisfying the escaping condition. Surprisingly, there may be infinitely many attracting periodic points for Hc. The set of such points gives rise to the dual Julia set, which is a Cantor set coming from a Conformal Iterated Funcion System. Both the Julia set and its dual are projections of holomorphic motions of dynamical systems (single valued maps) defined on compact subsets of Banach spaces, denoted by Xc and Wc, respectively. For c close to zero: (1) we show that Jc is a union of quasiconformal arcs around the unit circle; (2) the set Xc is an holomorphic motion of the solenoid X0; (3) using the formalism of Gibbs states we exhibit an upper bound for the Hausdorff dimension of Jc; which implies that Jc has zero Lebesgue measure. / Generalizamos as noções de estabilidade estrutural e hiperbolicidade para a família de correspondências holomorfas Hc(z) = zr + c; onde r > 1 é racional e zr = exp r log z: Descobrimos que Hc é estruturalmente estável em todos os parâmetros hiperbólicos satisfazendo a condição de fuga. Tipicamente Hc possui infinitos pontos periódicos atratores, fato totalmente inesperado, uma vez que este número é sempre finito para aplicações racionais. O conjunto de tais pontos dá origem ao chamado conjunto de Julia dual, que é um conjunto de Cantor proveniente de um Conformal Iterated Function System. Tanto o conjunto de Julia e quanto seu dual são projeções de movimentos holomorfos de sistemas definidos em subconjuntos compactos denotados por Xc e Wc; respectivamente de um espaço de Banach. Para todo c próximo de zero: (1) mostramos que Jc é reunião de arcos quase-conformes próximos do círculo unitário; (2) o conjunto Xc é um movimento holomorfo do solenóide X0; (3) utilizando o formalismo dos estados de Gibbs, exibimos um limitante superior para a dimensão de Hausdorff de Jc. Consequentemente, Jc possui medida de Lebesgue nula.

In 1939, composer Julia Smith's first opera Cynthia Parker dramatized the story of a Texas legend. Smith manipulated music, text, and visual images to make the opera accessible for the audience in accordance with compositional and institutional practices in American opera of the 1930s. Transparent musical themes and common Native Americans stereotypes are used to define characters. Folk music is presented as diegetic, creating a sense of authenticity that places the audience into the opera's Western setting. The opera is codified for the audience using popular idioms, resulting in initial but not lasting success.

Tato diplomová práce se zabývá tématikou konvexní optimalizace a to konkrétně modifikacemi algoritmu ADMM, společně s problematikou proximálních operátorů. Jedna z verzí ADMM je pak implementována v programovacím jazyce Julia s důrazem na obecnost a efektivnost této implementace, a dále aplikována na rozsáhlou úlohu z oblasti odpadového hospodářství.

This essay contains a discussion of my influences for making the choreographic work The Horrors of:, which was the practical part of an examination for the degree work of the bachelor’s Programme in Dance Performance at Stockholms Konstnärliga Högskola in the fall of 2022. The horrors of: is an exploration of women in horror and the potentiality of the monstrous feminine. Inspired by Julia Kristeva’s concept of abjection, Barbara Creed’s concept of the monstrous-feminine as well as films in the body horror genre, a search to represent the subjectivity of the women depicted in horror through dance emerged. In the body horror genre, the female characters are neither villains nor heroes, but complex characters who possess the capacity to both do good and destroy.    The text is divided in two parts: The first part dissects how the process was generated from researching the topics of femininity and abjection into a staged choreographic work and the second part contains a collage of poems along with other material collected from the artistic research process.

[pt] As atividades de transporte aéreo devem ser fiscalizadas para garantir a adequação dos níveis de segurança e procedimentos operacionais, no Brasil essa atividade é realizada pela Agência Nacional de Aviação Civil (ANAC). Diversos aeroportos devem ser fiscalizados e em cada um deles uma inspeção diferente pode ser necessária. Os inspetores estão alocados em centros da ANAC em diferentes estados e é importante que o custo dessa atividade de inspeção seja minimizado, respeitando as regras existentes. Nesse sentido, essa dissertação de mestrado propõe dois modelos matemáticos para alocação de agentes qualificados para a realização de missões de fiscalização no território brasileiro. O objetivo é a definição de quais colaboradores formarão cada equipe de fiscalização, minimizando o custo de deslocamento dos agentes. O modelo proposto nesse trabalho é multi-período, para o planejamento operacional quinzenal, com a definição do período que as atividades devem ocorrer, da equipe de inspetores multi-habilitados em atividades de inspeção, multi-origens e multi-destinos. A modelagem é feita no LINGO e em Julia com a utilização do pacote JuMP e dos solvers Gurobi e CPLEX. O Modelo 1 propõe uma reformulação de artigos da literatura e possui tempo de solução entre 2 e 25 vezes menor. O Modelo 2 leva em consideração aspectos não considerados até então no Modelo 1, além disso, dada a quantidade de variáveis de decisão, foi utilizada para resolução do modelo heurística baseada na geração de colunas com programação dinâmica, proposta pelo autor, capaz de reduzir em até 95 porcento a quantidade de variáveis de decisão. A heurística permitiu a obtenção de solução inteira em instâncias que não a obtiveram com o modelo completo. / [en] Air transport activities must be inspected to ensure the adequacy of safety levels and operating procedures, in Brazil this activity is carried out by the National Civil Aviation Agency (ANAC). Several airports must be inspected and at each airport a different inspection may be required. The inspectors are located in ANAC centers in different states and it is important that the cost of this inspection activity is minimized, respecting the existing rules. In this sense, this master s thesis proposes two mathematical models for the allocation of qualified workforce to carry out inspection missions in the Brazilian territory. The objective is to define which employees will form in each inspection team, minimizing the cost of displacement of agents. The model proposed in this work is multi-period, for fortnightly operational planning, with the definition of the period that the activities must occur, of a team of multiskilled inspectors in inspection activities, multi-sources and multi-destinations. Modeling is done in LINGO and Julia using the JuMP package and the solvers Gurobi and CPLEX. Model 1 proposes a reformulation of articles in the literature and has a solution time between 2 and 25 times shorter. The second model takes into account aspects not considered so far in Model 1, in addition, given the amount of decision variables, it was used to solve the heuristic model based on the generation of columns with dynamic programming, proposed by the author, capable of reducing by up to 95 percent the amount of decision variables. The heuristic allowed obtaining an integer solution in instances that did not have a solution with the complete model.

El propósito de la tesina presente es analizar la manera de expresar las dificultades de una identidad híbrida en dos poemas contemporáneos de dos escritoras de origen latinoamericano, Gloria Anzaldúa y Julia Alvarez. Se han analizado los dos poemas elegidos teniendo en cuenta la perspectiva de una identidad híbrida y los problemas que ello conlleva en una sociedad llena de normas y fronteras entre grupos étnicos, culturales y sexuales. Después del análisis de los poemas sigue una comparación entre los resultados de la investigación y finalmente presentamos nuestras conclusiones. El estudio muestra que a pesar de que los poemas parezcan muy diferentes se han encontrado puntos de relación, como por ejemplo la similitud de los mensajes principales de los poemas; que necesitamos aceptar las mezclas de culturas, etnias y sexos. / The purpose of this study is to analyse the expression of the difficulties with a hybrid identity in two contemporary poems written by two authors from Latin America, Gloria Anzaldúa and Julia Alvarez. The analysis of the two poems take into account the perspective of a hybrid identity and the problems that this entails in a society filled with rules, standards and boundaries between different ethnic, cultural and sexual groups.  The analysis of the two poems is followed by a comparison of the results of the investigation and ultimately is presented the conclusions. The study shows that the poems share several respects, despite that they at first seems very different. An example is the similarities of the main messages that the poems convey, that we need to accept the mix of cultures, ethnics and sexualities.

Cette thèse est constituée de cinq parties distinctes. La première partie est consacrée au problème de rigidité quasi-symétrique associé à un nouveau modèle de tapis de Sierpinski, qui ne sont pas quasi-symétriquement équivalent aux tapis de Sierpinski usuels. La seconde partie est une discussion portant sur la géométrie quasi-symétrique des ensembles de tapis de Julia, incluant en outre le quasi-cercle uniforme, ainsi que certaines propriétés de séparation uniforme. Lors de la troisième partie, nous déterminerons une condition permettant de savoir quand deux rayons externes d'un polynôme tendent vers un même point. Comme application, nous montrerons également la monotonie de l'entropie associée à une famille de polynômes quadratiques. La quatrième partie est inspirée du travail récent de Cui Guizhen et Tan Lei. En utilisant des outils classiques (module d'anneau et chirurgie quasi-conforme), nous étudierons la convergence de certains rayons en campagne locus espace des paramètres. Enfin, la dernière partie pore sur la famille des transformations de renormalisations générées. Plus précisément, cette partie abordera la connexité de ces ensembles de Julia, et le lieu de confinement dans l'espace des paramètres, ainsi que la formule asymptotique de la dimension d'Hausdorff des ensembles de Julia. / The thesis consists of five parts. The first part is concerned with the quasisymmetric rigidity of a new Sierpinski carpet, which are not quasis-ymmetrically equivalent to the standard Sierpinski carpets. The second part discusses the quasisymmetrically geometry of the carpet Julia sets, including the uniformly quasicircle and uniformly separated properties. The third part is to determine when two external rays of a polynomial land at the same point. As an application, we also show the monotonicity of core-entropy on a family of quadratic polynomials. In the fourth part, following Cui and Tan's work, we use the classic tools modulus of annulus and quasi-conformal surgery to study the landing of some parameter rays in shift locus parameter space. The last part discusses a family of generated renormal-ization transformations. Specifically, it is on the connec-tivity of its Julia sets and the non-escaping locus in its parameter space, the asymptotic formula of the Hausdorff dimention of the Julia sets.