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arXiv · 2507.10126

Polynomial entropy on the $n$-fold symmetric product and its suspension

Maša Đorić
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Abstract

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.

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Maša Đorić. 2025-07-14. Polynomial entropy on the $n$-fold symmetric product and its suspension. https://arxiv.org/abs/2507.10126

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