Polynomial entropy and expansivity
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- Artigue, A., Carrasco-Olivera, D. & Monteverde, I. Acta Math. Hungar. (2017) 152: 140. doi:10.1007/s10474-017-0689-3
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We study the polynomial entropy of homeomorphisms on compact metric spaces. 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 than or equal to 1.