Quasi-compactness and statistical properties for discontinuous systems semi-conjugate to piecewise convex maps with countably many branches
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916936541011968 |
|---|---|
| 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 |