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arXiv · 1207.4761

Statistical properties of generalized-Viana maps

Paulo Varandas
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Abstract

We study quadratic skew-products with parameters driven over piecewise expanding and Markov interval maps with countable many inverse branches, a generalization of the class of maps introduced by Viana. In particular we construct a class of multidimensional non-uniformly expanding attractors that exhibit both critical points and discontinuities and prove existence and uniqueness of an SRB measure with stretched-exponential decay of correlations, stretched-exponential large deviations and satisfying some limit laws. Moreover, generically such maps admit the coexistence of a dense subset of points with negative central Lyapunov exponent together with a full Lebesgue measure subset of points which have positive Lyapunov exponents in all directions. Finally, we discuss the existence of some non-uniformly hyperbolic attractors for skew-products associated to hyperbolic parameters.

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Paulo Varandas. 2013-03-31. Statistical properties of generalized-Viana maps. https://arxiv.org/abs/1207.4761

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