Statistical stability for robust classes of maps with non-uniform expansion. (English) Zbl 1067.37034

Alves, José F.; Viana, Marcelo

Ergodic Theory Dyn. Syst. 22, No. 1, 1-32 (2002).

The authors deal with properties of SRB measures. To this end, they consider open sets of transformations in a manifold \(\mathcal M\), exhibiting nonuniformly expanding behaviour in some invariant domain \(W\subset \mathcal M\). Under some suitable assumptions on each transformations the authors prove that the Sinai-Ruelle-Bowen (SRB) measure varies continuously with the dynamics in the \(L^1\) norm. The authors present a concrete application as well.

Reviewer: Messoud A. Efendiev (Berlin)

MSC:

37D25	Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37C30	Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc.

Keywords:

nonuniform expansion; stabiltiy; SRB measure