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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.
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