Stochastic stability of sectional-Anosov flows

Abstract

A {\em sectional-Anosov flow} is a vector field on a compact manifold inwardly transverse to the boundary such that the maximal invariant set is sectional-hyperbolic (in the sense of \cite{mm}). We prove that any $C^2$ transitive sectional-Anosov flow has a unique SRB measure which is stochastically stable under small random perturbations.

arXiv comment10 pages

References in corpus (1)

• SRB measure for higher dimensional singular partially hyperbolic flows

Cited by in corpus (2)

• Finitely many physical measures for sectional-hyperbolic attracting sets and statistical stability
• Noise induced order for skew-products over a non-uniformly expanding base