Uniqueness of the measure of maximal entropy for singular hyperbolic flows in dimension 3 and more results on equilibrium states

Abstract

We prove that any 3-dimensional singular hyperbolic attractor admits for any Hölder continuous potential $V$ at most one equilibrium state for $V$ among regular measures. We give a condition on $V$ which ensures that no singularity can be an equilibrium state. Thus, for these $V$'s, there exists a unique equilibrium state and it is a regular measure. Applying this for $V\equiv 0$, we show that any 3-dimensional singular hyperbolic attractor admits a unique measure of maximal entropy.

43 pages 14 figures

References in corpus (2)

• Existence and smoothness of the stable foliation for sectional hyperbolic attractors
• A minicourse on entropy theory on the interval