Dynamics of self-maps in their primal topologies
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915744651935744 |
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| author | Martin, Jose C. |
| author_facet | Martin, Jose C. |
| contents | We study a series of dynamical concepts for self-maps in the primal topology induced by them. Among the concepts studied are non-wandering points, limit points, recurrent points, minimal sets, transitive points and self-maps, topologically ergodic self-maps, weakly mixing self-maps, strongly mixing self-maps, Lyapunov stable self-maps, chaotic self-maps in the sense of Auslander-Yorke, chaotic self-maps in the sense of Devaney, asymptotic pairs, proximal pairs, and syndetically proximal pairs.
Some results are given in the more general context of continuous self-maps in an Alexandroff topological space. We prove that a continuous self-map of an Alexandroff space is always Lyapunov stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15264 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynamics of self-maps in their primal topologies Martin, Jose C. Dynamical Systems 37B02 (Primary) 37B20, 37B25, 54C99, 54F05, 54D10, 54E15 (Secondary) We study a series of dynamical concepts for self-maps in the primal topology induced by them. Among the concepts studied are non-wandering points, limit points, recurrent points, minimal sets, transitive points and self-maps, topologically ergodic self-maps, weakly mixing self-maps, strongly mixing self-maps, Lyapunov stable self-maps, chaotic self-maps in the sense of Auslander-Yorke, chaotic self-maps in the sense of Devaney, asymptotic pairs, proximal pairs, and syndetically proximal pairs. Some results are given in the more general context of continuous self-maps in an Alexandroff topological space. We prove that a continuous self-map of an Alexandroff space is always Lyapunov stable. |
| title | Dynamics of self-maps in their primal topologies |
| topic | Dynamical Systems 37B02 (Primary) 37B20, 37B25, 54C99, 54F05, 54D10, 54E15 (Secondary) |
| url | https://arxiv.org/abs/2601.15264 |