Polynomial Entropy and Expansivity

Alfonso Artigue, Dante Carrasco-Olivera, Ignacio Monteverde

Published 2018-01-26Version 1

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.