Original scientific paper

https://doi.org/10.3336/gm.61.1.03

Polynomial entropy on the \(n\)-fold symmetric product and its suspension

Maša Đorić ; Knez Mihailova 36, 11 000 Belgrade, Serbia

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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.

Keywords

Polynomial entropy, homeomorphism, hyperspace, \(n\)-fold symmetric product, symmetric product suspension

Hrčak ID:

348195

URI

https://hrcak.srce.hr/348195

Publication date:

30.6.2026.

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