Strong statistical stability of non-uniformly expanding maps

By José F. Alves. Nonlinearity, 2003

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We consider families of transformations in multidimensional Riemannian manifolds with non-uniformly expanding behaviour. We give sufficient conditions for the continuous variation (in the L1-norm) of the densities of absolutely continuous (with respect to the Lebesgue measure) invariant probability measures for those transformations.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e2b34c6886b56ea15dd55ddfaef360289eef0ceb