Acta Mathematica Hungarica

, Volume 152, Issue 1, pp 140–149

Polynomial entropy and expansivity


DOI: 10.1007/s10474-017-0689-3

Cite this article as:
Artigue, A., Carrasco-Olivera, D. & Monteverde, I. Acta Math. Hungar. (2017) 152: 140. doi:10.1007/s10474-017-0689-3


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.

Key words and phrases

topological entropy polynomial entropy expansivity 

Mathematics Subject Classification

primary 37B40 28D20 37A35 secondary 37B10 37B45 54H20 37C10 

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  • A. Artigue
    • 1
  • D. Carrasco-Olivera
    • 2
  • I. Monteverde
    • 1
  1. 1.Departamento de Matemática y Estadística del LitoralUniversidad de la RepúblicaSaltoUruguay
  2. 2.Grupo de Investigación en Sistemas Dinámicos y Aplicaciones, Departamento de MatemáticaFacultad de Ciencias, Universidad del Bío BíoConcepciónChile

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