Piecewise Contractions
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915232757055488 |
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| author | Jain, Sakshi Liverani, Carlangelo |
| author_facet | Jain, Sakshi Liverani, Carlangelo |
| contents | We study piecewise injective, but not necessarily globally injective, contracting maps on a compact subset of \(\bR^d\). We prove that generically the attractor and the set of discontinuities of such a map are disjoint, and hence the attractor consists of periodic orbits. In addition, we prove that piecewise injective contractions are generically topologically stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02371 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Piecewise Contractions Jain, Sakshi Liverani, Carlangelo Dynamical Systems We study piecewise injective, but not necessarily globally injective, contracting maps on a compact subset of \(\bR^d\). We prove that generically the attractor and the set of discontinuities of such a map are disjoint, and hence the attractor consists of periodic orbits. In addition, we prove that piecewise injective contractions are generically topologically stable. |
| title | Piecewise Contractions |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2404.02371 |