pith. sign in

arxiv: 1209.2008 · v1 · pith:WYNFYDHAnew · submitted 2012-09-10 · 🧮 math.DS

Thermodynamic formalism for Lorenz maps

classification 🧮 math.DS
keywords goodleaveslorenzmeasuresproveunionallowsattractor
0
0 comments X
read the original abstract

For a 2-dimensional map representing an expanding geometric Lorenz at- tractor we prove that the attractor is the closure of a union of as long as possible unstable leaves with ending points. This allows to define the notion of good measures, those giving full measure to the union of these open leaves. Then, for any H\"older continuous potential we prove that there exists at most one relative equilibrium state among the set of good measures. Condition yielding existence are given.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.