Nesta sexta-feira (28/11) teremos uma tarde de seminários internos do Grupo de Dinâmica da UFF. Todos os interessados são bem vindos. As palestras acontecerão na Pós-Graduação em Matemática da UFF, no auditório da Pós-Graduação (sala 407), quarto andar do Bloco H, campus do Gragoatá.
Seguem abaixo os detalhes:
Jiagang Yang: 13h
Ledrappier-Young entropy formula for C^1 diffeomorphisms with dominated splitting Part 1: Unstable entropy formula and invariance principle
This is a joint work with Shaobo Gan and Yao Tong.
We study the unstable entropy of C1 diffeomorphisms with dominated splittings. Our main result shows that when the zero Lyapunov exponent has multiplicity one, the center direction contributes no entropy, and the unstable entropy coincides with the metric entropy. This extends the celebrated work of Ledrappier-Young [18] for C2 diffeomorphisms to the C1 setting under these assumptions. In particular, our results apply to C1 diffeomorphisms away from homoclinic tangencies due to [20].
As consequences, we obtain several applications at C1 regularity. The Avila-Viana invariance principle [7, 33] holds when the center is one-dimensional. Results on measures of maximal entropy due to Hertz-Hertz-Tahzibi-Ures [25], Tahzibi-Yang [33], and Ures-Viana-Yang-Yang [34, 35] also remain valid for C1 diffeomorphisms.
Bruno Santiago: 14h
O fluxo instável de um difeomorfismo parcialmente hiperbólico
Resumo: Dado um difeomorfismo parcialmente hiperbólico de codimensão 1, é possível parametrizar sua folheação instável de modo que as medidas u-Gibbs se tornem medidas invariantes pelo fluxo obtido? Vou apresentar uma proposta de solução para esse problema que passa por aumentar a dimensão do ambiente e tomar uma suspensão adequada da dinâmica. Se o tempo permitir, vou apresentar algumas ideias sobre como usar esse fluxo para provar um teorema de unicidade de medidas u-Gibbs. Trabalho em andamento com Sébastien Alvarez, Sylvain Crovisier, Martin Leguil e Davi Obata.
Café: 15h
Pablo Barrientos: 15h30
Kingman and Uniform Kingman Subadditive Ergodic Theorems for Markov Operators
Resumo: The Subadditive Ergodic Theorem, introduced by Kingman, provides a powerful and indispensable generalization of the classical Birkhoff Ergodic Theorem, particularly suitable for studying products of random matrices or random processes in general. In this talk, we will present the precise statements of two fundamental and deep results: the classical Kingman Subadditive Ergodic Theorem and its less common yet highly effective extension, the Uniform Kingman Subadditive Ergodic Theorem, adapted to the general setting of Markov operators. These theorems serve as the unifying foundation for a variety of major results in ergodic theory and stochastic processes, which we will explore through their applications. Namely, we discuss the Mean Ergodic Theorems, the Breiman-Kifer-Furstenberg Law of Large Numbers, and the Furstenberg-Kifer formula for the representation of the Lyapunov exponent. The presented results and their applications come from a joint work with Dominique Malicet entitled “Mostly contracting random maps.”