English

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 ϕ\phi, we prove that for an open and dense subset of C1C^1 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}
}