Absolutely continuous invariant measures for non-expanding maps

Details Absolutely continuous invariant measures for non-expanding maps Absolutely continuous invariant measures for non-expanding maps

2011-11-19

arxiv.org/abs/1111.4540v1

Mathematics

Dynamical Systems

24 pages; 2 figures

Scientific paper

We prove existence of absolutely continuous invariant probability measures for skew-products with arbitrary base dynamics and asymptotic expansion along the one-dimensional fibers. We also prove a similar result for skew-product maps having higher-dimensional fibers with essentially arbitrary base dynamics and non-uniform expansion along the fibers. In both cases either critical or singular points on the dynamics along the fibers are admitted.

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