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

Abstract

We prove that the polynomial entropy of the induced map Fn(f ) on the n-fold symmetric product of a compact space X and its sus- pension are both equal to nhpol(f ), when f : X → X is a homeomorphism with a finite chain recurrent set 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.