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Statistical stability for Hénon maps of the Benedicks-Carleson type. (English) Zbl 1205.37040

This paper deals with a family \(\{f_{a,b}\}_{(a,b)\in{\mathcal BC}}\) of Hénon maps in the plane given by \((x,y)\mapsto (1-ax^2+y,bx)\). The parameters \((a,b)\) are allowed in a set \({\mathcal BC}\) where, as shown by Benedicks and Carleson, the Hénon conjecture on the existence of strange attractors holds.
The main result of the paper states that the map associating each \((a,b)\in{\mathcal BC}\) to the corresponding Sinai-Ruelle-Bowen (SRB) measure is continuous with respect to the weak-* topology in the space of probability measures.

MSC:

37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems
37C75 Stability theory for smooth dynamical systems
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
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