Title: Uniqueness of equilibrium states for sectional-hyperbolic flows, including the classical Lorenz attractor
Speaker: Prof. Yang Fan, Wake Forest University
Time: Friday, 3:30-4:30 pm, June 23, 2023
Venue: Jingzhai 105
It has long been conjectured that the classical Lorenz attractor supports a unique measure of maximal entropy. In this talk, we will give a positive answer to this conjecture and its higher-dimensional counterpart by considering the uniqueness of equilibrium states for H\"older continuous functions on a sectional-hyperbolic attractor. we will prove that on every compact manifold with dimension at least three, there exists a $C^1$-open and dense family of vector fields that includes the classical Lorenz attractor (when $\dim M=3$), such that if the point masses at singularities are not equilibrium states, then there exists a unique equilibrium state. In particular, there exists a unique measure of maximal entropy. This is joint work with Maria Jose Pacifico and Jiagang Yang.