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

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.

31 pages, 13 figures

References in corpus (3)

• Existence and smoothness of the stable foliation for sectional hyperbolic attractors
• A non-autonomous flow system with Plykin type attractor
• Upper large deviations bound for singular-hyperbolic attracting sets

Cited by in corpus (1)

• Physical measures for mostly sectional expanding flows