Polynomial entropy on the $n$-fold symmetric product and its suspension
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914340456628224 |
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| author | Đorić, Maša |
| author_facet | Đorić, Maša |
| contents | We prove that the polynomial entropy of the induced map $F_n(f)$ on the $n$-fold symmetric product of a compact space $X$ and its suspension are both equal to $nh_{pol}(f)$, when $f:X\to X$ is a homeomorphism with a finite chain recurrent set $\mathcal{CR}(f)$. We also give a lower bound for the polynomial entropy on the suspension, for a homeomorphism $f$ with at least one wandering point, under certain assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10126 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polynomial entropy on the $n$-fold symmetric product and its suspension Đorić, Maša Dynamical Systems 37B40, 54F16 We prove that the polynomial entropy of the induced map $F_n(f)$ on the $n$-fold symmetric product of a compact space $X$ and its suspension are both equal to $nh_{pol}(f)$, when $f:X\to X$ is a homeomorphism with a finite chain recurrent set $\mathcal{CR}(f)$. We also give a lower bound for the polynomial entropy on the suspension, for a homeomorphism $f$ with at least one wandering point, under certain assumptions. |
| title | Polynomial entropy on the $n$-fold symmetric product and its suspension |
| topic | Dynamical Systems 37B40, 54F16 |
| url | https://arxiv.org/abs/2507.10126 |