Na próxima semana o Matéo Ghezal (Université Paris-Saclay) vai visitar o IME-UFF e dar um minicurso de quatro aulas a respeito do seu trabalho recente que demonstra a finitude de medidas de máxima entropia para endomorfismos suaves de superfícies com entropia alta. Os encontros ocorrerão de segunda à quinta-feira a partir das 13h30 na Pós-Graduação em Matemática da UFF (Bloco H, Campus do Gragoatá, 4º Andar). Nos dias 27, 28 e 30 o curso será realizado no auditório (sala 407) e no dia 29 será realizado na sala 401.
Seguem abaixo as informações:
Title: Measures of Maximal Entropy for Smooth Entropy-Saddle Surface Endomorphisms
Abstract: The goal of this mini-course is to review the proof of the finiteness of the set of measures of maximal entropy for smooth entropy-saddle surface endomorphisms, and to understand the techniques developed to analyze these measures. Here, a smooth surface endomorphism is said to be entropy-saddle if its topological entropy is greater than the logarithm of its topological degree. The proof is divided into several steps. First, we construct families of well-behaved geometric rectangles exhibiting a Markov property. The second part consists of a topological analysis of the intersection of a curve with such rectangles, in order to obtain bounds on the number of rectangles needed to cover the curve. Finally, we will implement entropy arguments to establish homoclinic relations along sequences of measures whose entropy converges to the topological entropy.