# zbMATH — the first resource for mathematics

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

##### 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
Full Text: