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arXiv · 1905.06202

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

Renaud Leplaideur
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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.

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Renaud Leplaideur. 2019-05-15. Uniqueness of the measure of maximal entropy for singular hyperbolic flows in dimension 3 and more results on equilibrium states. https://arxiv.org/abs/1905.06202

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