1. The omega limit sets of subsets in a metric space
- Creator:
- Ding, Changming
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- limit set of a set, attractor, quasi-attractor, and hyperspace
- Language:
- English
- Description:
- 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 $\lbrace (\mathop {\mathrm Cl}Y)\cdot [i,\infty )\rbrace _{i=1}^{\infty }$ 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public