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SRB measures for non-hyperbolic systems with multidimensional expansion. (English) Zbl 0955.37012
The main goal of this work is to set up a framework for the study of statistical properties of systems with nonuniform expansion, which is motivated by the examples of multidimensional nonhyperbolic attractors constructed by M. Viana. The approach involves an inducing procedure, based on the notion of hyperbolic time that he introduces here, and contains a theorem of existence of absolutely continuous invariant measures for multidimensional piecewise expanding maps with countably many domains of smoothness.

MSC:
37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37A05 Dynamical aspects of measure-preserving transformations
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