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

Fuente: arXiv
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Main Author: Lucena, Rafael
Format: Preprint
Published: 2025
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author Lucena, Rafael
author_facet Lucena, Rafael
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2502_08751
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Quasi-compactness and statistical properties for discontinuous systems semi-conjugate to piecewise convex maps with countably many branches
Lucena, Rafael
Dynamical Systems
37A25, 37A30, 37H05
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.
title Quasi-compactness and statistical properties for discontinuous systems semi-conjugate to piecewise convex maps with countably many branches
topic Dynamical Systems
37A25, 37A30, 37H05
url https://arxiv.org/abs/2502.08751