Dynamical Systems Seminar

Equilibrium states for the classical Lorenz attractor and sectional-hyperbolic attractors in higher dimensions

  • 演讲者:杨佳刚(巴西弗鲁米嫩塞联邦大学)

  • 时间:2023-03-13 10:30-11:30

  • 地点:台州楼233B


This is a joint work with Maria Jose Pacifico and Fan Yang.

It has long been conjectured that the classical Lorenz attractor supports a unique measure of maximal entropy. In this article, we give a positive answer to this conjecture and its higher-dimensional counterpart by considering the uniqueness of  equilibrium states for Hölder continuous functions on a sectional-hyperbolic attractor Λ. We prove that in a C1-open and densely family of vector fields (including the classical Lorenz attractor), if the point masses at singularities are not equilibrium states, then there exists a unique equilibrium state supported on Λ. In particular, there exists a unique measure of maximal entropy for the flow X|Λ.