EQUILIBRIUM STATES FOR THE CLASSICAL LORENZ ATTRACTOR AND SECTIONAL-HYPERBOLIC ATTRACTORS IN HIGHER DIMENSIONS
报告人：Jiagang Yang (Universidade Federal Fluminense, Brazil)
时间：2023-02-27 15:10-17:00
地点：Room 1304, Sciences Building No. 1
Abstract: This ia 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 $\Lambda$. We prove that in a $C^1$-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 $\Lambda$. In particular, there exists a unique measure of maximal entropy for the flow $X|_\Lambda$.
