Glasnik Matematicki, Vol. 61, No. 1 (2026), 59-76. \( \)

POLYNOMIAL ENTROPY ON THE \(n\)-FOLD SYMMETRIC PRODUCT AND ITS SUSPENSION

Maša Đorić

Knez Mihailova 36, 11 000 Belgrade, Serbia
e-mail:masha@mi.sanu.ac.rs

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.

2020 Mathematics Subject Classification.   37B40, 54F16, 37A35

Key words and phrases.   Polynomial entropy, homeomorphism, hyperspace, \(n\)-fold symmetric product, symmetric product suspension

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

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