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

Tatiane Cardoso Batista, Juliano dos Santos Gonschorowski, and Fabio Armando Tal. "Density of the set of symbolic dynamics with all ergodic measures supported on periodic orbits." Fundamenta Mathematicae 231.1 (2015): 93-99. <http://eudml.org/doc/283068>.

@article{TatianeCardosoBatista2015,
abstract = {Let K be the Cantor set. We prove that arbitrarily close to a homeomorphism T: K → K there exists a homeomorphism T̃: K → K such that the ω-limit of every orbit is a periodic orbit. We also prove that arbitrarily close to an endomorphism T: K → K there exists an endomorphism T̃: K → K with every orbit finally periodic.},
author = {Tatiane Cardoso Batista, Juliano dos Santos Gonschorowski, Fabio Armando Tal},
journal = {Fundamenta Mathematicae},
keywords = {ergodic measures; Cantor set; periodic orbits},
language = {eng},
number = {1},
pages = {93-99},
title = {Density of the set of symbolic dynamics with all ergodic measures supported on periodic orbits},
url = {http://eudml.org/doc/283068},
volume = {231},
year = {2015},
}

TY - JOUR
AU - Tatiane Cardoso Batista
AU - Juliano dos Santos Gonschorowski
AU - Fabio Armando Tal
TI - Density of the set of symbolic dynamics with all ergodic measures supported on periodic orbits
JO - Fundamenta Mathematicae
PY - 2015
VL - 231
IS - 1
SP - 93
EP - 99
AB - Let K be the Cantor set. We prove that arbitrarily close to a homeomorphism T: K → K there exists a homeomorphism T̃: K → K such that the ω-limit of every orbit is a periodic orbit. We also prove that arbitrarily close to an endomorphism T: K → K there exists an endomorphism T̃: K → K with every orbit finally periodic.
LA - eng
KW - ergodic measures; Cantor set; periodic orbits
UR - http://eudml.org/doc/283068
ER -