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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.07642 |
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| _version_ | 1866914161657643008 |
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| author | Pereira, Rafael Da C. Vales, Túlio Morais, Cássio H. Vieira |
| author_facet | Pereira, Rafael Da C. Vales, Túlio Morais, Cássio H. Vieira |
| contents | In this paper, we study the dynamics of set-valued maps whose graphs are open and such that the image of each point is an open and connected set. Building upon the work of P. Duarte and M. Torres, who introduced and analyzed the combinatorial structure of the final recurrent set, we incorporate the notions of transitivity and mixing, thereby bringing their framework into the spirit of Smale's spectral decomposition theorem. We also demonstrate that such maps exhibit infinite topological entropy, and we establish a connection between transitive open set-valued maps and transitive Anosov diffeomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral decomposition and entropy for open set-valued maps Pereira, Rafael Da C. Vales, Túlio Morais, Cássio H. Vieira Dynamical Systems In this paper, we study the dynamics of set-valued maps whose graphs are open and such that the image of each point is an open and connected set. Building upon the work of P. Duarte and M. Torres, who introduced and analyzed the combinatorial structure of the final recurrent set, we incorporate the notions of transitivity and mixing, thereby bringing their framework into the spirit of Smale's spectral decomposition theorem. We also demonstrate that such maps exhibit infinite topological entropy, and we establish a connection between transitive open set-valued maps and transitive Anosov diffeomorphisms. |
| title | Spectral decomposition and entropy for open set-valued maps |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2511.07642 |