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
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
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
Affiliations des auteurs :
Tatiane Cardoso Batista 1 ; Juliano dos Santos Gonschorowski 1 ; Fabio Armando Tal 2
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author = {Tatiane Cardoso Batista and Juliano dos Santos Gonschorowski and Fabio Armando Tal},
title = {Density of the set of symbolic dynamics
with all ergodic measures supported on periodic orbits},
journal = {Fundamenta Mathematicae},
pages = {93--99},
publisher = {mathdoc},
volume = {231},
number = {1},
year = {2015},
doi = {10.4064/fm231-1-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm231-1-6/}
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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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