Equilibrium states for the classical Lorenz attractor and sectional-hyperbolic attractors in higher dimensions
Maria Jose Pacifico (UFRJ)

It has long been conjectured that the classical Lorenz attractor supports a unique measure of maximal entropy. In this talk, 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 sectionalhyperbolic attractor Λ. We prove that in a C1-open and dense 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. This corresponds to a joint work with Fan Yang and Jiagang Yang.