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Density of the set of symbolic dynamics with all ergodic measures supported on periodic orbits

Volume 231 / 2015

Tatiane Cardoso Batista, Juliano dos Santos Gonschorowski, Fabio Armando Tal Fundamenta Mathematicae 231 (2015), 93-99 MSC: Primary 37B10; Secondary 37A05, 37D35. DOI: 10.4064/fm231-1-6

Abstract

Let $K$ be the Cantor set. We prove that arbitrarily close to a homeomorphism $T:K\rightarrow K$ there exists a homeomorphism $\widetilde T:K\rightarrow K$ such that the $\omega$-limit of every orbit is a periodic orbit. We also prove that arbitrarily close to an endomorphism $T:K\rightarrow K$ there exists an endomorphism $\widetilde T:K\rightarrow K$ with every orbit finally periodic.

Authors

  • Tatiane Cardoso BatistaUniversidade Tecnológica Federal do Paraná
    85053-525 Guarapuava, Brazil
    e-mail
  • Juliano dos Santos GonschorowskiUniversidade Tecnológica Federal do Paraná
    85053-525 Guarapuava, Brazil
    e-mail
  • Fabio Armando TalInstituto de Matemática e Estatística
    Universidade de São Paulo
    05508-090 São Paulo, Brazil
    e-mail

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