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On Families of Bowen – Series-Like Maps for Surface Groups

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Abstract

We review some recent results on a class of maps, called Bowen – Series-like maps, obtained from a class of group presentations for surface groups. These maps are piecewise homeomorphisms of the circle with finitely many discontinuities. The topological entropy of each map in the class and its relationship with the growth function of the group presentation is discussed, as well as the computation of these invariants.

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  • 29 October 2023

    The numbering issue has been changed to 4-5.

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Funding

This work has been possible due to the financial support of our respective institutions, the MICINN grant number PID2020-118281GB-C31 and the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M) funded by MCIN/AEI/10.13039/501100011033. We thank CERCA Programme/Generalitat de Catalunya for institutional support.

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Authors and Affiliations

  1. Departament de Matemàtiques, Campus de Bellaterra, Edifici C, 08193, Barcelona, Spain

    Lluís Alsedà & Francesc Mañosas

  2. Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, 08193, Barcelona, Spain

    Lluís Alsedà

  3. Departament d’Informàtica i Matemàtica Aplicada, Universitat de Girona, c/ de la Universitat de Girona, 6, 17003, Girona, Spain

    David Juher

  4. 3 place Victor Hugo, 13331, Marseille Cedex 3, France

    Jérôme Los

Authors
  1. Lluís Alsedà
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  2. David Juher
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  3. Jérôme Los
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  4. Francesc Mañosas
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Corresponding authors

Correspondence to Lluís Alsedà, David Juher, Jérôme Los or Francesc Mañosas.

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The authors declare that they have no conflicts of interest.

Additional information

This paper is dedicated to Alain Chenciner on the occasion of his 80th birthday

MSC2010

57M07, 57M05, 37E10, 37B40, 37B10

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Alsedà, L., Juher, D., Los, J. et al. On Families of Bowen – Series-Like Maps for Surface Groups. Regul. Chaot. Dyn. 28, 659–667 (2023). https://doi.org/10.1134/S1560354723040093

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  • DOI: https://doi.org/10.1134/S1560354723040093

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