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1
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MARIANA TAVARES DE AGUIAR
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SCALING LIMITS FOR SLOWED EXCLUSION PROCESS
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Líder : TERTULIANO FRANCO SANTOS FRANCO
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MIEMBROS DE LA BANCA :
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CLAUDIO LANDIM
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DIRK ERHARD
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MILTON DAVID JARA VALENZUELA
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PAULO CESAR RODRIGUES PINTO VARANDAS
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TERTULIANO FRANCO SANTOS FRANCO
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Data: 28-ene-2019
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Resumen Espectáculo
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The aim of the present study was to study the following problems: Hydrodynamic Limit for SSEP with a slow membrane and Out of Balance Fluctuations for SSEP with a slow link. More precisely, the hydrodynamic boundary study model is the symmetric simple exclusion process (SSEP) in the d-dimensional torus, which has a membrane whose passage rate $? / (N ^?) $, $? > 0 $, is lower than the rate in other links. Due to the existence of this slow membrane, depending on the regimen of the parameter that regulates the slowness of this membrane, border conditions appear at macroscopic level. For $ \ beta \ in [0, 1) $, the hydrodynamic equation is given by the heat equation in the continuous torus, meaning that the slow membrane has no effect on the boundary. For $ \ in \ (1, \ infty) $, the hydrodynamic equation is given by the heat equation with Neumann edge conditions, meaning that the membrane divides the torus into two isolated regions. And, for the critical value $ \ beta = 1 $, the hydrodynamic equation is given by the heat equation with Robin boundary conditions, related to Fick's law. In the case of Fluctuations, the model under study is the one-dimensional SSEP that has a slow link. The great difficulty in the work of the Fluctuations was to obtain accurate estimates of transition probabilities of random walks of dimensions 1 and 2.
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2
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ADRIANA COUTINHO DOS SANTOS
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Asymptotic probabilistic properties of orbits: return times and shortest distance
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Líder : JEROME FRANCOIS ALAIN JEAN ROUSSEAU
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MIEMBROS DE LA BANCA :
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BENOIT SAUSSOL
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JEROME FRANCOIS ALAIN JEAN ROUSSEAU
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MIGUEL NATALIO ABADI
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PAULO CESAR RODRIGUES PINTO VARANDAS
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RODRIGO LAMBERT
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Data: 15-feb-2019
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Resumen Espectáculo
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This work provides some original contributions to the study of large deviation for return times and the asymptotic behavior of the shortest distance between observed orbits. In the first part, we prove a large deviation result for return time of the orbits of a dynamical system in a r-neighbourhood of an initial point x. Our first result may be seen as a differentiable version of the work by Jain and Bansal, who considered the return time of a stationary and ergodic process defined in the space of infinite sequences. We obtain large deviation estimates for dynamical systems in general and in the case of conformal repellers we compute the rate functions in terms of HP-spectrum for dimensions of multifractal analysis. In the second part of this work, we investigate the shortest distance between two observed orbits and its asymptotic behavior. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the correlation dimension of the pushforward measure. We apply this result to study the shortest distance between orbits of a random dynamical system. In the symbolic case, this problem corresponds to the longest common substring problem for encoded sequences and its limiting relationship with the R´enyi entropy. We apply this results to the zero-inflated contamination model and to the stochastic scrabble.
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3
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GERALDO DE ASSIS JUNIOR
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ON MINIMALITY OF THE SYMMETRICAL AND STANDARD POLYNOMONES IN ALGEBRAS VERBALLY PRIMAS.
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Líder : THIERRY CORREA PETIT LOBAO
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MIEMBROS DE LA BANCA :
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FERNANDA GONÇALVES DE PAULA
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KARINA KFOURI SARTORI
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MANUELA DA SILVA SOUZA
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SÉRGIO MOTA ALVES
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THIERRY CORREA PETIT LOBAO
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Data: 04-abr-2019
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Resumen Espectáculo
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The present work brings as an object of study the minimality of the degree of symmetric and standard polynomials in verbal raw algebras. That said, we determine the minimal degree of the symmetric polynomial that makes it a polynomial identity for the algebras M_n (E), M_ (a, b) (E), and A_ (a, b) (E). For the standard polynomial, we determine its minimal degree in the ideal T-algebra M_ (n, n) (E) and set altitudes for the algebras M_n (E), M_ (a, b) (E), and A_ (a, b) (E) advanced the results of papers already published (ALVES; SARTORI, 2015, 2017; ALVES; ASSIS, 2017). We also study the minimal degree of the symmetric and standard polynomials in the tensor power of Grassmann's algebra E ^ (⊗ ^ n) = E ⊗ ⋯ ⊗E (n factors), generalizing a result of Gaimbruno and Koshlukov (2001). Then, the minimal degree of the symmetric polynomial in the ideal T-T of E ^ (⊗ ^ n) and the minimal degree of the standard polynomial in the ideal T of E ^ (⊗ ^ 2n) were determined, and finally we determined the degrees minimal of the standard polynomial so that it belongs to the ideal T of E ^ (⊗ ^ (2n + 1)).
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4
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5
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VINICIUS COELHO DOS SANTOS
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Some topics about singular hyperbolicity and invariant measures
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Líder : LUCIANA SILVA SALGADO
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MIEMBROS DE LA BANCA :
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LUCIANA SILVA SALGADO
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VILTON JEOVAN VIANA PINHEIRO
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VITOR DOMINGOS MARTINS DE ARAUJO
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FELIPE FONSECA DOS SANTOS
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MANUEL STADLBAUER
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Data: 18-abr-2019
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Resumen Espectáculo
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We showed the existence of singular adapted metrics for any codimension one singular hyperbolic set with respect to a $C^1 vector field on finite dimensional compact manifolds without using quadradic forms. Looking at the measures of a system, we provided a Kingman-like Theorem for an arbitrary finite measure assuming some conditions in any metric space, and we give necessary conditions to guarantee the existence of invariant measures in locally compact and separable metric spaces for continuous proper maps. Moreover, we use the Perron-Frobenius operator and the techniques developed here to obtain other criteria to guarantee the existence of invariant measures for continuous maps (not necessarily a proper maps) in locally compact separable metric spaces.
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6
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JUNILSON CERQUEIRA DA SILVA
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Komuro-expansiveness for sectional-hyperbolic attracting sets
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Líder : VITOR DOMINGOS MARTINS DE ARAUJO
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MIEMBROS DE LA BANCA :
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VITOR DOMINGOS MARTINS DE ARAUJO
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VILTON JEOVAN VIANA PINHEIRO
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AUGUSTO ARMANDO DE CASTRO JUNIOR
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LUCIANA SILVA SALGADO
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FELIPE FONSECA DOS SANTOS
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Data: 06-jun-2019
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Resumen Espectáculo
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In this work we prove the expansiveness according to Komuro for hyperbolic-sectional measures for a variety of dimension d ≥ 3. For this we present two results, the first is restricted to the case in that d_cu = 2, that is, the center-unstable subfibre of the sink has dimensions are 2 and the second is for the case d_cu> 2. In the latter case we will see that it is necessary to assume that the sink is 1-strongly dissipative. However, Poincaré, our main tool for study of expansivity, and we used stable foliation throughout the region trap containing the sink to analyze expansion of distances. We also present some consequences of these results.
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7
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ELAINE FERREIRA ROCHA
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Extension of Kesten's criterion on amenity for extensions by Gibbs-Markov application graph
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Líder : AUGUSTO ARMANDO DE CASTRO JUNIOR
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MIEMBROS DE LA BANCA :
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ALBERT MEADS FISHER
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MANUEL STADLBAUER
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TERTULIANO FRANCO SANTOS FRANCO
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VILTON JEOVAN VIANA PINHEIRO
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VITOR DOMINGOS MARTINS DE ARAUJO
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Data: 24-sep-2019
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Resumen Espectáculo
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This paper provides some original contributions to the study of the relationships between graph amenity and Dynamic Systems. In the first main result of the work, we characterize graph amenity through the extension by graph of a complete Markov application, inspired by the works of Stadlbauer and Jaerisch for extension by group. We saw that under soft hypotheses, the graph is mild if, and only if, the spectral radius of the Transfer operator associated with graph extension is equal to 1. In addition, we have defined graph extension of Markov applications with embedded Gibbs Markov structure and non-uniformly expandable applications, and we show the graph amenity characterization through graph extension for these classes of dynamic systems. We conclude with two non-trivial applications. First, we show that Schreier's graph is mild, if the decay rate of the graph extension of a Markov application with embedded Gibbs-Markov structure is equal to 1, while in the other application, we consider an extension of a complete Markov application by a semigroup. In this scenario, the amenity of the semigroup is equivalent to the spectral radius of the Transfer operator equal to 1.
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8
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SARA RUTH PIRES BISPO
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Martin's frontier of an extension by a hyperbolic group
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Líder : AUGUSTO ARMANDO DE CASTRO JUNIOR
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MIEMBROS DE LA BANCA :
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LEANDRO MARTINS CIOLETTI
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MANUEL STADLBAUER
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TERTULIANO FRANCO SANTOS FRANCO
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VILTON JEOVAN VIANA PINHEIRO
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VITOR DOMINGOS MARTINS DE ARAUJO
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Data: 12-nov-2019
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Resumen Espectáculo
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Ancona-Gouëzel uniform inequalities established for random walk in hyperbolic groups were extended to extension by hyperbolic group. As application, we obtained the identification of the minimum conforming measures with the visual border of the hyperbolic group. In the first main result of the work, these inequalities were established. For this purpose, it was necessary to generalize Green's functions to the extensions by hyperbolic groups, through Green's family of operators. As an application, a Hölder function was obtained from the visual boundary to the Martin boundary. In order to obtain an analogous function in the reverse direction, proving that both boundaries are homeomorph bi-Hölder, a family of conforming and minimal measures was defined. Martin's border has been shown to coincide with this set of measures.
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