Characterization of $\omega$-limit sets of continuous maps of the circle

Pokluda, David. "Characterization of $\omega $-limit sets of continuous maps of the circle." Commentationes Mathematicae Universitatis Carolinae 43.3 (2002): 575-581. <http://eudml.org/doc/248990>.

@article{Pokluda2002,
abstract = {In this paper we extend results of Blokh, Bruckner, Humke and Sm’ıtal [Trans. Amer. Math. Soc. 348 (1996), 1357–1372] about characterization of $\omega $-limit sets from the class $\mathcal \{C\}(I,I)$ of continuous maps of the interval to the class $\mathcal \{C\}(\mathbb \{S\},\mathbb \{S\})$ of continuous maps of the circle. Among others we give geometric characterization of $\omega $-limit sets and then we prove that the family of $\omega $-limit sets is closed with respect to the Hausdorff metric.},
author = {Pokluda, David},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {dynamical system; circle map; $\omega $-limit set; dynamical system; circle map; -limit set},
language = {eng},
number = {3},
pages = {575-581},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Characterization of $\omega $-limit sets of continuous maps of the circle},
url = {http://eudml.org/doc/248990},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Pokluda, David
TI - Characterization of $\omega $-limit sets of continuous maps of the circle
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 3
SP - 575
EP - 581
AB - In this paper we extend results of Blokh, Bruckner, Humke and Sm’ıtal [Trans. Amer. Math. Soc. 348 (1996), 1357–1372] about characterization of $\omega $-limit sets from the class $\mathcal {C}(I,I)$ of continuous maps of the interval to the class $\mathcal {C}(\mathbb {S},\mathbb {S})$ of continuous maps of the circle. Among others we give geometric characterization of $\omega $-limit sets and then we prove that the family of $\omega $-limit sets is closed with respect to the Hausdorff metric.
LA - eng
KW - dynamical system; circle map; $\omega $-limit set; dynamical system; circle map; -limit set
UR - http://eudml.org/doc/248990
ER -