The Artin-Mazur zeta function for interval maps
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917669865783296 |
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| author | Olivares-Vinales, Jorge |
| author_facet | Olivares-Vinales, Jorge |
| contents | In this work we study the Artin-Mazur zeta function for piecewise monotone functions acting on a compact interval of real numbers. In the case of unimodal maps, Milnor and Thurston gave a characterization for the rationality of the Artin-Mazur zeta function in terms of the orbit of the unique turning point. We show that for multimodal maps, the previous characterization does not hold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Artin-Mazur zeta function for interval maps Olivares-Vinales, Jorge Dynamical Systems 37E05, 37E15, 37F44 In this work we study the Artin-Mazur zeta function for piecewise monotone functions acting on a compact interval of real numbers. In the case of unimodal maps, Milnor and Thurston gave a characterization for the rationality of the Artin-Mazur zeta function in terms of the orbit of the unique turning point. We show that for multimodal maps, the previous characterization does not hold. |
| title | The Artin-Mazur zeta function for interval maps |
| topic | Dynamical Systems 37E05, 37E15, 37F44 |
| url | https://arxiv.org/abs/2405.10560 |