Quasi-compactness and statistical properties for discontinuous systems semi-conjugate to piecewise convex maps with countably many branches
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916936541011968 |
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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 |