Speaker:<\/strong> Sebastian Burgos (Penn State University) Speaker:<\/strong> Neemias Martins Speaker: <\/strong>Matheus Cunhas Speaker:<\/strong> Matheus Cunha Speaker:<\/strong> Matias Zimmermann <\/p>\n\n\n\n Speaker:<\/strong> Paulo Lupatini Speaker:<\/strong> Ygor de Jesus Speaker:<\/strong> Eduarda Dutra de Almeida x’=Ax+n+<\/sup>, se h(x)>0,<\/p>\n\n\n\n x’= Bx+n\u2212<\/sup>, se h(x)<0, Speaker:<\/strong> Pedro Campos Speaker:<\/strong> Felipe Carvalho Silva <\/p>\n<\/div>\n\n\n\n Speaker:<\/strong> Let\u00edcia C\u00e2ndido Speaker:<\/strong> Pedro Mattos Speaker:<\/strong> Ewerton Rocha Vieira (Rutgers University and UFG) Speaker:<\/strong> Ygor de Jesus (Unicamp) On the structure of the Birkhoff-irregular set for some subshifts of finite type Speaker: Sebastian Burgos (Penn State University)Abstract: We study the set of irregular points for Birkhoff averages for a class of topologically mixing subshifts of finite type. It is well known that, despite the irregular set having zero measure for every invariant measure, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-9","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.ime.unicamp.br\/dynsys\/index.php\/wp-json\/wp\/v2\/pages\/9"}],"collection":[{"href":"https:\/\/www.ime.unicamp.br\/dynsys\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.ime.unicamp.br\/dynsys\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.ime.unicamp.br\/dynsys\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ime.unicamp.br\/dynsys\/index.php\/wp-json\/wp\/v2\/comments?post=9"}],"version-history":[{"count":24,"href":"https:\/\/www.ime.unicamp.br\/dynsys\/index.php\/wp-json\/wp\/v2\/pages\/9\/revisions"}],"predecessor-version":[{"id":118,"href":"https:\/\/www.ime.unicamp.br\/dynsys\/index.php\/wp-json\/wp\/v2\/pages\/9\/revisions\/118"}],"wp:attachment":[{"href":"https:\/\/www.ime.unicamp.br\/dynsys\/index.php\/wp-json\/wp\/v2\/media?parent=9"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Abstract:<\/strong> We study the set of irregular points for Birkhoff averages for a class of topologically mixing subshifts of finite type. It is well known that, despite the irregular set having zero measure for every invariant measure, it possesses full topological entropy and Hausdorff dimension. We establish that for these systems, the irregular set is not only abundant in its dimensional properties but also contains uncountably many pairwise disjoint subsets, each with full entropy and dimension.
Date:<\/strong> 19\/11\/2024 – 16:00
Room:<\/strong> https:\/\/meet.google.com\/hhk-vvch-vdk<\/a><\/p>\n\n\n\nExtended Symbolic Dynamics: Entropies and the Isomorphism problem<\/h2>\n\n\n\n
Abstract:<\/strong> In this talk, we present a symbolic dynamical system defined in a locally invertible context and show how its folding and Kolmogorov-Sinai entropies are related. We use these results to study the isomorphism problem of extended Bernoulli maps following Ornstein’s techniques.
Date:<\/strong> 12\/11\/2024 – 16:00
Room:<\/strong> 321 IMECC<\/p>\n\n\n\nHyperbolicity for Infinite Delayed Difference Equations<\/h2>\n\n\n\n
Abstract:<\/strong> We show that the hyperbolicity of a linear delay-difference equation with infinite delay, expressed in terms of the existence of an exponential dichotomy, can be completely characterized by the hyperbolicity of a linear cocycle obtained from the solutions of the equation. As an appli-
cation of this characterization, we obtain several consequences: the extension of hyperbolicity to all equations in the invariant hull; the robustness of the existence of hyperbolicity for all equations in this hull under sufficiently small linear perturbations; and the equality of all spectra in the invariant hull.
Date:<\/strong> 29\/10\/2024 – 16:00
Room:<\/strong> 321 IMECC<\/p>\n\n\n\nGeometry of Shilnikov connections in Filippov Spaces<\/h2>\n\n\n\n
Abstract:<\/strong> The concept of sliding Shilnikov connection has been recently introduced and represents an important notion in Filippov systems, because its existence implies chaotic behavior on an invariant subset of the system. The investigation of its properties has just begun, and understanding the topology and complexity of its invariant set is of interest. We conduct a local analysis on the first return map associated to a Shilnikov sliding connection, which reveals a conformal iterated function system (CIFS) structure. By using the theory of CIFS, we estimate the Hausdorff dimension of the local invariant set of the first return map, showing, in particular, that it is strictly greater than 0 and strictlyless than 1, and its one-dimensional Lebesgue measure is 0. Moreover, we prove that the closure of the local invariant set is a Cantor set and has the same Hausdorff dimension and Lebesgue measure of the original invariant set. Furthermore, it is given by the invariant set adjoined with the set of all pre-imagesof the regular-fold point. At last, we discuss some topological and ergodic properties.
Date:<\/strong> 22\/10\/2024
Room:<\/strong> 321 IMECC<\/p>\n\n\n\nRandom Dynamical Systems: An Introduction<\/h2>\n\n\n\n
Abstract:<\/strong> The main purpose of this short seminar is to present and popularize the notion of a Random Dynamical System (RDS) and to give an impression of its scope. The concept of a RSD is an extension of the deterministic concept of a dynamical system, and it reduces to the latter if it does not depend on a stochastic term. Informally, the theory considers the random composition of different maps chosen from a typical sequence of transformations. A natural question in the study of these systems is how can we describe these chaotic phenomena in random dynamical systems? The answer to this question can be dealt with by employing the random thermodynamic formalism developed in recent years.
Date:<\/strong> 15\/10\/2024 – 16:00
Room:<\/strong> 321 IMECC<\/p>\n\n\n\nEntropy for compact operators and results on entropy and specification<\/h2>\n\n\n\n
Abstract:<\/strong> We prove that the specification property implies infinite topological entropy for operators acting on infinite dimensional $F$-spaces. We also prove that compact operators acting on Banach spaces have finite entropy and the entropy depends exclusively on the operators point spectrum. Additionally, we prove that the variational principle is not valid for compact operators acting on Banach spaces.
Date:<\/strong> 08\/10\/2024 – 16:00
Room:<\/strong> 321 IMECC<\/p>\n\n\n\nConstruction of Partially Hyperbolic Geodesic Flows via conformal deformation<\/h2>\n\n\n\n
Abstract:<\/strong> In this talk we are going to present a construction of examples of partially hyperbolic geodesic flows that are not of Anosov type. This problem was first approached by Car- neiro and Pujals. Their construction is based on deforming the Riemannian metric along a closed geodesic in order to break the hyperbolic behavior. Based on their work, we propose a new construction with several advantages to analyze the remaining hyperbolic behavior. With the new construction, we can have finer curvature estimates and prove ergodicity in some cases. Besides that, we present a criterion for obtaining robustly transitive geodesic flow inside this class. For the robust transitivity criterion, we present a new notion of SH-saddle property. As a consequence of these results, we can observe new behaviors for the geodesic flow in manifolds with conjugate points.
Date:<\/strong> 01\/10\/2024 – 16:00
Room:<\/strong> 321 IMECC<\/p>\n\n\n\nConex\u00e3o de Shilnikov Em Sistemas Lineares Por Partes em R3<\/sup>.<\/h2>\n\n\n\n
Abstract:<\/strong> Neste trabalho, estudamos a exist\u00eancia e unicidade de conex\u00f5es homocl\u00ednicas em sistemas de equa\u00e7\u00f5es diferenciais ordin\u00e1rias suaves por partes da forma<\/p>\n\n\n\n
onde x \u2208 R3<\/sup>, a fun\u00e7\u00e3o h \u00e9 expressa por h(x) = z e x’ denota a derivada em rela\u00e7\u00e3o ao tempo t. Al\u00e9m disso, A, B \u2208 M3<\/sub>(R) e n\u00b1<\/sup> = (n1<\/sub>\u00b1<\/sup> , n2<\/sub>\u00b1<\/sup> , n3<\/sub>\u00b1<\/sup> ) s\u00e3o a matriz e o vetor de par\u00e2metros, respectivamente, com cada aij<\/sub>, ni<\/sub>\u00b1<\/sup> \u2208 R. Em particular, analisamos a ocorr\u00eancia de uma conex\u00e3o homocl\u00ednica, do tipo Shilnikov, para sistemas de equa\u00e7\u00f5es diferenciais ordin\u00e1rias lineares por partes em R3<\/sup>.
Date:<\/strong> 24\/09\/2024 – 16:00
Room:<\/strong> 321 IMECC<\/p>\n\n\n\nBifurca\u00e7\u00f5es e cat\u00e1strofes<\/h2>\n\n\n\n
Abstract:<\/strong> A teoria de bifurca\u00e7\u00f5es de sistemas din\u00e2micos estuda a mudan\u00e7a de retratos de fase causada pela mudan\u00e7a de par\u00e2metros de um sistema. Em geral, o conceito de equival\u00eancia topol\u00f3gica \u00e9 utilizada para identificar retratos de fase “similares” e propor uma classifica\u00e7\u00e3o de bifurca\u00e7\u00f5es baseada em quais mudan\u00e7as s\u00e3o observadas nas classes de equival\u00eancia obtidas. A expans\u00e3o de tal classifica\u00e7\u00e3o para casos mais complexos, por\u00e9m, traz consigo uma mir\u00edade de problemas t\u00e9cnicos que at\u00e9 hoje esperam solu\u00e7\u00e3o. Nessa apresenta\u00e7\u00e3o, vamos discutir o conceito de equival\u00eancia de contato como uma ferramenta que ajuda a compreender bifurca\u00e7\u00f5es, incluindo um resultado recente.
Date:<\/strong> 17\/09\/2024 – 16:00
Room:<\/strong> https:\/\/meet.google.com\/awm-frzk-pzy<\/a><\/p>\n\n\n\nIntrodu\u00e7\u00e3o a Espa\u00e7os Uniformes e Aplica\u00e7\u00f5es<\/h2>\n\n\n\n
Abstract:<\/strong> Continuidade uniforme \u00e9 um importante conceito para muitas das \u00e1reas da matem\u00e1tica, usualmente estudada em termos de uma m\u00e9trica. Naturalmente, podemos nos questionar se \u00e9 poss\u00edvel generalizar essa defini\u00e7\u00e3o para espa\u00e7os mais gerais, presumidamente espa\u00e7os topol\u00f3gicos. Surpreendentemente e diferente da continuidade, a continuidade uniforme n\u00e3o \u00e9 proveniente da topologia e requer uma estrutura adicional no espa\u00e7o para poder ser abordada. Essa estrutura \u00e9 chamada uniformidade e nos permite explorar diversas propriedades gerais, assim como uma topologia nos permite explorar propriedades da continuidade. Essa palestra tem como objetivo introduzir o conceito de Espa\u00e7os Uniformes; apresentar algumas das “propriedades uniformes”, isto \u00e9, propriedades preservadas por transforma\u00e7\u00f5es uniformes, e, por fim, expor poss\u00edveis aplica\u00e7\u00f5es dessa estrutura em pesquisas atuais. A saber, no contexto da din\u00e2mica de operadores, entropia topol\u00f3gica e caos linear, mas que podem certamente ser aplicadas em outros cen\u00e1rios.
Date:<\/strong> 10\/09\/2024 – 16:00
Room:<\/strong> 321 IMECC<\/p>\n\n\n\nUma introdu\u00e7\u00e3o ao \u00cdndice de Conley<\/h2>\n\n\n\n
Abstract:<\/strong> A teoria do \u00edndice de Conley tornou-se uma ferramenta importante no estudo qualitativo de equa\u00e7\u00f5es diferenciais, onde pode-se estudar a estrutura local de um conjunto isolado e invariante. Tal \u00edndice pode ser definido no contexto mais geral de um fluxo cont\u00ednuo em um espa\u00e7o topol\u00f3gico. A teoria de Conley j\u00e1 foi bem explorada no contexto de fluxos de Morse em variedades fechadas. Nesse contexto, os \u00edndices de Conley fornecem uma f\u00f3rmula alternativa para um importante invariante topol\u00f3gico, a caracter\u00edstica de Euler da variedade. Al\u00e9m disso, temos uma rela\u00e7\u00e3o com o \u00edndice de Poincare-Hopf associado a singularidades isoladas de um campo vetorial em uma variedade suave, i.e., quando a caracter\u00edstica de Euler de uma variedade M \u00e9 a soma sobre todas as singularidades isoladas do campo vetorial definido em M. Com isso, o \u00edndice de Conley, uma ferramenta da topologia alg\u00e9brica, consegue nos fornecer resultados importantes sobre variedades e fluxos definidos em tais variedades.
Date:<\/strong> 03\/09\/2024 – 16:00
Room:<\/strong> 321 IMECC<\/p>\n\n\n\nCaos n\u00e3o determin\u00edstico em sistemas din\u00e2micos suaves por partes<\/strong><\/h3>\n\n\n\n
Abstract:<\/strong> Nosso contexto s\u00e3o campos vetoriais suaves por partes (CVSP) definidos em variedades bidimensionais com um n\u00famero finito de pontos de tang\u00eancia. Provamos que transitividade topol\u00f3gica \u00e9 uma condi\u00e7\u00e3o necess\u00e1ria e suficiente para a ocorr\u00eancia de caos n\u00e3o determin\u00edstico quando o sistema do CVSP tem regi\u00f5es de deslize e escape n\u00e3o vazias. Um resultado fundamental para fluxos cont\u00ednuos \u00e9 a equival\u00eancia de transitividade topol\u00f3gica e a exist\u00eancia de uma \u00f3rbita densa. Provamos, no nosso contexto, que transitividade topol\u00f3gica para sistemas de CVSP \u00e9 de fato equivalente \u00e0 exist\u00eancia de uma \u00f3rbita densa, embora, em contraste com o caso do fluxo cont\u00ednuo, n\u00e3o consigamos garantir que a \u00f3rbita densa implique a exist\u00eancia de um conjunto residual de \u00f3rbitas densas. Finalmente, provamos que, nesse contexto, transitividade topol\u00f3gica implica entropia topol\u00f3gica estritamente positiva para o sistema do CVSP. Esse c\u00e1lculo \u00e9 feito usando t\u00e9cnicas similares \u00e0quelas da din\u00e2mica simb\u00f3lica.
Date:<\/strong> 27\/08\/2024 – 16:00
Room:<\/strong> 321 IMECC<\/p>\n\n\n\nAdvances in Computing the Global Dynamics of ODE<\/strong><\/h3>\n\n\n\n
Abstract:<\/strong> In this talk, we explore the challenges faced in analyzing time-varying systems with multi-scale dynamics. While traditional methods model these systems using ordinary differential equations (ODE), the direct analysis of such models is often difficult due to poorly measured parameters and numerous variables. To overcome these challenges, we propose a novel approach based on combinatorics and algebraic topology. We move away from classical ODE analysis and focus toward a more robust, scalable, and computable description of global dynamics in terms of annotated graphs (Morse graphs) and Conley complexes.
Date:<\/strong> 20\/08\/2024 – 16:00
Room:<\/strong> 321 IMECC<\/p>\n\n\n\nQuando o fluxo geod\u00e9sico \u00e9 do tipo Anosov?<\/strong><\/h2>\n\n\n\n
Abstract:<\/strong> O fluxo geod\u00e9sico de uma superf\u00edcie de curvatura negativa \u00e9 um dos mais antigos exemplos de fluxos com a propriedade de ergodicidade. \u00c9 conhecido que fluxos geod\u00e9sicos do tipo Anosov em dimens\u00e3o arbitr\u00e1ria apresentam propriedades ainda mais gerais do que ergodicidade, em especial tais fluxos s\u00e3o conjugados a um shift de Bernoulli. Em particular, fluxos geod\u00e9sicos do tipo Anosov s\u00e3o exemplos cl\u00e1ssicos de fluxos mixing. Devido a riqueza de propriedades din\u00e2micas e erg\u00f3dicas para essa classe particular de fluxos, \u00e9 interessante estudar condi\u00e7\u00f5es equivalentes a condi\u00e7\u00e3o de Anosov neste contexto. Essa quest\u00e3o foi investigada por Patrick Eberlein em uma s\u00e9rie de c\u00e9lebres artigos publicados nos anos 70 e intitulados “When is the geodesic flow of Anosov type? I” e “When is the geodesic flow of Anosov type? II”. Neste semin\u00e1rio apresentaremos a geometria elementar para o estudo de fluxos geod\u00e9sicos e os elementos que comp\u00f5e o primeiro artigo de Eberlein.
Date:<\/strong> 13\/08\/2024 – 16:00
Room:<\/strong> 321 IMECC<\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"