Periodic Points of Ruelle-Expanding Maps

• Maria Pires de Carvalho ^[1] ; Mário Alexandre Magalhães ^[1]
  1. [1] Universidade Do Porto

     Universidade Do Porto

     Santo Ildefonso, Portugal

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 13, Nº 2, 2014, págs. 215-251
• Idioma: inglés
• DOI: 10.1007/s12346-014-0115-y
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• Resumen

  • A Ruelle-expanding map is an open continuous transformation defined on a compact metric space which expands distances locally. For such dynamical systems, we will explain why: (a) the zeta function is rational; (b) the topological entropy is equal to the exponential growth rate of the periodic points; (c) the topological entropy is positive unless the domain of the map is finite. These properties have been remarked in the work of D. Ruelle but without entering into all the necessary details; the aim of this text is precisely to provide them.