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arXiv · 2204.10084

On the number of ergodic physical/SRB measures of singular-hyperbolic attracting sets

Vitor Araujo
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Abstract

It is known that sectional-hyperbolic attracting sets, for a $C^2$ flow on a finite dimensional compact manifold, have at most finitely many ergodic physical invariant probability measures. We prove an upper bound for the number of distinct ergodic physical measures supported on a connected singular-hyperbolic attracting set for a $3$-flow. This bound depends only on the number of Lorenz-like equilibria contained in the attracting set. Examples of singular-hyperbolic attracting sets are provided showing that the bound is sharp.

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Vitor Araujo. 2022-04-21. On the number of ergodic physical/SRB measures of singular-hyperbolic attracting sets. https://doi.org/10.1016/j.jde.2023.02.008

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