On strong chain recurrence for maps

Katsuya Yokoi. "On strong chain recurrence for maps." Annales Polonici Mathematici 114.2 (2015): 165-177. <http://eudml.org/doc/280718>.

@article{KatsuyaYokoi2015,
abstract = {This paper is concerned with strong chain recurrence introduced by Easton. We investigate the depth of the transfinite sequence of nested, closed invariant sets obtained by iterating the process of taking strong chain recurrent points, which is a related form of the central sequence due to Birkhoff. We also note the existence of a Lyapunov function which is decreasing off the strong chain recurrent set. As an application, we give a necessary and sufficient condition for the coincidence of the strong chain recurrence set and the chain recurrence set. Several examples are given to illustrate the difference between the concepts of strong chain recurrence and chain recurrence.},
author = {Katsuya Yokoi},
journal = {Annales Polonici Mathematici},
keywords = {(strong) chain recurrence; Lyapunov function; depth},
language = {eng},
number = {2},
pages = {165-177},
title = {On strong chain recurrence for maps},
url = {http://eudml.org/doc/280718},
volume = {114},
year = {2015},
}

TY - JOUR
AU - Katsuya Yokoi
TI - On strong chain recurrence for maps
JO - Annales Polonici Mathematici
PY - 2015
VL - 114
IS - 2
SP - 165
EP - 177
AB - This paper is concerned with strong chain recurrence introduced by Easton. We investigate the depth of the transfinite sequence of nested, closed invariant sets obtained by iterating the process of taking strong chain recurrent points, which is a related form of the central sequence due to Birkhoff. We also note the existence of a Lyapunov function which is decreasing off the strong chain recurrent set. As an application, we give a necessary and sufficient condition for the coincidence of the strong chain recurrence set and the chain recurrence set. Several examples are given to illustrate the difference between the concepts of strong chain recurrence and chain recurrence.
LA - eng
KW - (strong) chain recurrence; Lyapunov function; depth
UR - http://eudml.org/doc/280718
ER -