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arXiv · 2209.04907

Mixing implies exponential mixing among codimension one hyperbolic attractors and Anosov flows

Vitor Araujo
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Abstract

On a compact manifold of any dimension $d\geq 3$, we show that joint non-integrability of the stable and unstable foliation of a hyperbolic attractor with one-dimensional expanding direction, for a vector field of class $C^2$, implies exponential mixing with respect to its physical measure. Consequently, the set of Axiom A vector fields which mix exponentially with respect to the physical measure of its non-trivial attractors contains a $C^1$-open and $C^2$-dense subset of the set of all Axiom A vector fields. Moreover, for codimension one $C^2$ Anosov flows in any dimension $d\geq 3$, if the flow mixes with respect to the unique physical measure, then the flow mixes exponentially, proving the Bowen-Ruelle conjecture in this setting.

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Vitor Araujo. 2022-09-11. Mixing implies exponential mixing among codimension one hyperbolic attractors and Anosov flows. https://arxiv.org/abs/2209.04907

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