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arXiv · 2502.08751

Quasi-compactness and statistical properties for discontinuous systems semi-conjugate to piecewise convex maps with countably many branches

Rafael Lucena
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Abstract

In this paper, we establish the quasi-compactness of the transfer operator associated with skew product systems that are semi-conjugate to piecewise convex maps with a countably infinite number of branches. These non-invertible skew products admit discontinuities, with the critical set confined to a countable collection of fibers. Furthermore, we demonstrate that such systems possess an invariant measure whose disintegration along the fibers exhibits bounded variation; a concept introduced and developed in this work.

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Rafael Lucena. 2025-02-12. Quasi-compactness and statistical properties for discontinuous systems semi-conjugate to piecewise convex maps with countably many branches. https://doi.org/10.3934/dcds.2025108

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