Polynomial Entropy and Expansivity

2018/01/26 by Artigue, Alfonso, Carrasco-Olivera, Dante, Monteverde, Ignacio · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.08774

Abstract

In this paper we study the polynomial entropy of homeomorphism on compact metric space. We construct a homeomorphism on a compact metric space with vanishing polynomial entropy that it is not equicontinuous. Also we give examples with arbitrarily small polynomial entropy. Finally, we show that expansive homeomorphisms and positively expansive maps of compact metric spaces with infinitely many points have polynomial entropy greater or equal than 1.

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

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