Quasi-compactness and statistical properties for discontinuous systems semi-conjugate to piecewise convex maps with countably many branches
Dynamical Systems
2025-09-09 v9
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.
Keywords
Cite
@article{arxiv.2502.08751,
title = {Quasi-compactness and statistical properties for discontinuous systems semi-conjugate to piecewise convex maps with countably many branches},
author = {Rafael Lucena},
journal= {arXiv preprint arXiv:2502.08751},
year = {2025}
}
Comments
Corrections were limited to metadata adjustments