Dynamical Systems Seminar

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

  • Speaker: Jiagang Yang (Universidade Federal Fluminense, Brazil)

  • Time: Mar 13, 2023, 10:30-11:30

  • Location: 233B, Taizhou Hall


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.