The structure of $\omega$-limit sets for continuous maps of the interval

Bruckner, Andrew M., and Smítal, Jaroslav. "The structure of $\omega $-limit sets for continuous maps of the interval." Mathematica Bohemica 117.1 (1992): 42-47. <http://eudml.org/doc/29394>.

@article{Bruckner1992,
abstract = {We prove that every infinite nowhere dense compact subset of the interval $I$ is an $\omega $-limit set of homoclinic type for a continuous function from $I$ to $I$.},
author = {Bruckner, Andrew M., Smítal, Jaroslav},
journal = {Mathematica Bohemica},
keywords = {discrete dynamical system; continuous map; $\omega $-limit set; homoclinic set; discrete dynamical system; continuous map; -limit set; homoclinic set},
language = {eng},
number = {1},
pages = {42-47},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The structure of $\omega $-limit sets for continuous maps of the interval},
url = {http://eudml.org/doc/29394},
volume = {117},
year = {1992},
}

TY - JOUR
AU - Bruckner, Andrew M.
AU - Smítal, Jaroslav
TI - The structure of $\omega $-limit sets for continuous maps of the interval
JO - Mathematica Bohemica
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 117
IS - 1
SP - 42
EP - 47
AB - We prove that every infinite nowhere dense compact subset of the interval $I$ is an $\omega $-limit set of homoclinic type for a continuous function from $I$ to $I$.
LA - eng
KW - discrete dynamical system; continuous map; $\omega $-limit set; homoclinic set; discrete dynamical system; continuous map; -limit set; homoclinic set
UR - http://eudml.org/doc/29394
ER -