Uniqueness of equilibrium states for Lorenz attractors in any dimension
Dynamical Systems
2022-01-19 v1
Abstract
In this note, we consider the thermodynamic formalism for Lorenz attractors of flows in any dimension. Under a mild condition on the H\"older continuous potential function , we prove that for an open and dense subset of vector fields, every Lorenz attractor supports a unique equilibrium state. In particular, we obtain the uniqueness for the measure of maximal entropy.
Keywords
Cite
@article{arxiv.2201.06622,
title = {Uniqueness of equilibrium states for Lorenz attractors in any dimension},
author = {Maria Jose Pacifico and Fan Yang and Jiagang Yang},
journal= {arXiv preprint arXiv:2201.06622},
year = {2022}
}