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

@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 -