Polynomial entropy of induced homeomorphisms on $C_k(\mathbb{S}^1)$ and $C_k([0,1])$
We compute the polynomial entropy of $C_k(f)$ where $f$ is any circle or interval homeomorphism.
math.DS↗
arXiv subjects
Maša Đorić
Publications and source records attributed to Maša Đorić.
A flexibility result for polynomial entropy of pointwise periodic homeomorphisms
We construct a family of continua and pointwise periodic homeomorphisms realizing arbitrary polynomial entropy values in $[0,+\infty]$. In particular, this provides examples of pointwise periodic homeomorphisms with positive polynomial entropy. This contrasts with the fact that pointwise periodic homeomorphisms on connected manifolds and local dendrites have zero polynomial entropy.
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Polynomial entropy on the $n$-fold symmetric product and its suspension
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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Polynomial entropy on regular curves
We show that the polynomial entropy of homeomorphisms on regular curves is bounded above by one. Moreover, the polynomial entropy equals one under the fairly mild condition that the homeomorphism possesses a wandering point. We obtain a rigidity result for homeomorphisms on local dendrites (and therefore on graphs and dendrites): their polynomial entropy is either zero or one.
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