Geodesic
Density of the set of symbolic dynamics with all ergodic measures supported on periodic orbits
Tatiane Cardoso Batista 1   ; Juliano dos Santos Gonschorowski 1   ; Fabio Armando Tal 2
1 Universidade Tecnológica Federal do Paraná 85053-525 Guarapuava, Brazil
2 Instituto de Matemática e Estatística Universidade de São Paulo 05508-090 São Paulo, Brazil
Fundamenta Mathematicae, Tome 231 (2015) no. 1, pp. 93-99 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm231-1-6
Keywords: cantor set prove arbitrarily close homeomorphism rightarrow there exists homeomorphism widetilde rightarrow omega limit every orbit periodic orbit prove arbitrarily close endomorphism rightarrow there exists endomorphism widetilde rightarrow every orbit finally periodic

Tatiane Cardoso Batista  1   ; Juliano dos Santos Gonschorowski  1   ; Fabio Armando Tal  2

1 Universidade Tecnológica Federal do Paraná 85053-525 Guarapuava, Brazil
2 Instituto de Matemática e Estatística Universidade de São Paulo 05508-090 São Paulo, Brazil 
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     title = {Density of the set of symbolic dynamics
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     journal = {Fundamenta Mathematicae},
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Tatiane Cardoso Batista; Juliano dos Santos Gonschorowski; Fabio Armando Tal. Density of the set of symbolic dynamics
 with all ergodic measures supported on periodic orbits. Fundamenta Mathematicae, Tome 231 (2015) no. 1, pp. 93-99. doi: 10.4064/fm231-1-6

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