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Polynomial entropy and expansivity

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Abstract

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.

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Authors and Affiliations

  1. Departamento de Matemática y Estadística del Litoral, Universidad de la República, Gral. Rivera 1350, Salto, Uruguay

    A. Artigue & I. Monteverde

  2. Grupo de Investigación en Sistemas Dinámicos y Aplicaciones, Departamento de Matemática, Facultad de Ciencias, Universidad del Bío Bío, Av. Collao 1202, Casilla 5-C, Concepción, Chile

    D. Carrasco-Olivera

Authors
  1. A. Artigue
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  2. D. Carrasco-Olivera
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  3. I. Monteverde
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Corresponding author

Correspondence to D. Carrasco-Olivera.

Additional information

The second author was supported by CONICYT-Chile, project FONDECYT 11121598.

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Artigue, A., Carrasco-Olivera, D. & Monteverde, I. Polynomial entropy and expansivity. Acta Math. Hungar. 152, 140–149 (2017). https://doi.org/10.1007/s10474-017-0689-3

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  • DOI: https://doi.org/10.1007/s10474-017-0689-3

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