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arXiv · 2209.10784

Equilibrium states for the classical Lorenz attractor and sectional-hyperbolic attractors in higher dimensions

Maria Jose Pacifico·Fan Yang·Jiagang Yang
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Abstract

It has long been conjectured that the classical Lorenz attractor supports a unique measure of maximal entropy. In this article, we give a positive answer to this conjecture and its higher-dimensional counterpart by considering the uniqueness of equilibrium states for H\"older continuous functions on a sectional-hyperbolic attractor $\Lambda$. We prove that in a $C^1$-open and dense family of vector fields (including the classical Lorenz attractor), if the point masses at singularities are not equilibrium states, then there exists a unique equilibrium state supported on $\Lambda$. In particular, there exists a unique measure of maximal entropy for the flow $X|_\Lambda$.

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Maria Jose Pacifico, Fan Yang, Jiagang Yang. 2022-09-22. Equilibrium states for the classical Lorenz attractor and sectional-hyperbolic attractors in higher dimensions. https://arxiv.org/abs/2209.10784

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