报告摘要: How often does it occur that the measure of maximal entropy of a system is an SRB measure? We will talk about this question for C1+α partially hyperbolic diffeomorphisms isotopic to Anosov (DA-diffeomorphisms) on T3, and establish a rigidity result: the measure of maximal entropy is an SRB measure if and only if the sum of its positive Lyapunov exponents coincides with that of the linear Anosov map A on all periodic orbits of the support of the measure.
We will also show that a volume-preserving C1+α DA diffeomorphism on T3 is Anosov if all Lyapunov exponents coincide almost everywhere with those of the linear Anosov in its isotopy class. Consequently, a smooth DA diffeomorphism is smoothly conjugated to its linear part if and only if all Lyapunov exponents coincide almost everywhere with those of its linear part.
This talk is based in a joint work with Fernando Micena, Ryo Moore, and Jana R. Hertz.
个人简介：Raul Ures completed his PhD studies at IMPA, Rio de Janeiro. He was a professor at the University of the Republic, Uruguay, and is currently a professor at the Southern University of Science and Technology in Shenzhen. He has been selected for China’s national talent initiatives and Shenzhen’s "Peacock Plan" for high-level overseas talents. He has several publications in prestigious journals such as Inventiones Mathematicae, Acta Mathematica, Duke Mathematical Journal, etc. His main research areas are dynamical systems and ergodic theory.
