Fixed point indices of iterates of orientation-reversing homeomorphisms
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915236369399808 |
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| author | Graff, Grzegorz Topór, Patryk |
| author_facet | Graff, Grzegorz Topór, Patryk |
| contents | We show that any sequence of integers satisfying necessary Dold's congruences is realized as the sequence of fixed point indices of the iterates of an orientation-reversing homeomorphism of $\mathbb{R}^{m}$ for $m\geq 3$. As an element of the construction of the above homeomorphism, we consider the class of boundary-preserving homeomorphisms of $\mathbb{R}^{m}_{+}$ and give the answer to [Problem 10.2, Topol. Methods Nonlinear Anal. 50 (2017), 643 - 667] providing a complete description of the forms of fixed point indices for this class of maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08753 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fixed point indices of iterates of orientation-reversing homeomorphisms Graff, Grzegorz Topór, Patryk Dynamical Systems Primary 37B30, 55M20, Secondary 37E30 We show that any sequence of integers satisfying necessary Dold's congruences is realized as the sequence of fixed point indices of the iterates of an orientation-reversing homeomorphism of $\mathbb{R}^{m}$ for $m\geq 3$. As an element of the construction of the above homeomorphism, we consider the class of boundary-preserving homeomorphisms of $\mathbb{R}^{m}_{+}$ and give the answer to [Problem 10.2, Topol. Methods Nonlinear Anal. 50 (2017), 643 - 667] providing a complete description of the forms of fixed point indices for this class of maps. |
| title | Fixed point indices of iterates of orientation-reversing homeomorphisms |
| topic | Dynamical Systems Primary 37B30, 55M20, Secondary 37E30 |
| url | https://arxiv.org/abs/2409.08753 |