The omega limit sets of subsets in a metric space
Czechoslovak Mathematical Journal (2005)
- Volume: 55, Issue: 1, page 87-96
- ISSN: 0011-4642
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topDing, Changming. "The omega limit sets of subsets in a metric space." Czechoslovak Mathematical Journal 55.1 (2005): 87-96. <http://eudml.org/doc/30928>.
@article{Ding2005,
abstract = {In this paper, we discuss the properties of limit sets of subsets and attractors in a compact metric space. It is shown that the $\omega $-limit set $\omega (Y)$ of $Y$ is the limit point of the sequence $\lbrace (\mathop \{\mathrm \{C\}l\}Y)\cdot [i,\infty )\rbrace _\{i=1\}^\{\infty \}$ in $2^X$ and also a quasi-attractor is the limit point of attractors with respect to the Hausdorff metric. It is shown that if a component of an attractor is not an attractor, then it must be a real quasi-attractor.},
author = {Ding, Changming},
journal = {Czechoslovak Mathematical Journal},
keywords = {limit set of a set; attractor; quasi-attractor; hyperspace; limit set of a set; attractor; quasi-attractor; hyperspace},
language = {eng},
number = {1},
pages = {87-96},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The omega limit sets of subsets in a metric space},
url = {http://eudml.org/doc/30928},
volume = {55},
year = {2005},
}
TY - JOUR
AU - Ding, Changming
TI - The omega limit sets of subsets in a metric space
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 1
SP - 87
EP - 96
AB - In this paper, we discuss the properties of limit sets of subsets and attractors in a compact metric space. It is shown that the $\omega $-limit set $\omega (Y)$ of $Y$ is the limit point of the sequence $\lbrace (\mathop {\mathrm {C}l}Y)\cdot [i,\infty )\rbrace _{i=1}^{\infty }$ in $2^X$ and also a quasi-attractor is the limit point of attractors with respect to the Hausdorff metric. It is shown that if a component of an attractor is not an attractor, then it must be a real quasi-attractor.
LA - eng
KW - limit set of a set; attractor; quasi-attractor; hyperspace; limit set of a set; attractor; quasi-attractor; hyperspace
UR - http://eudml.org/doc/30928
ER -
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