Chain transitivity, attractivity, and strong repellors for semidynamical systems

Morris W. Hirsch; Hal Smith; Xiao Qiang Zhao

doi:10.1023/A:1009044515567

Chain transitivity, attractivity, and strong repellors for semidynamical systems

Morris W. Hirsch, Hal Smith, Xiao Qiang Zhao

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

156 Scopus citations

Abstract

Some properties of internally chain transitive sets for continuous maps in metric spaces are presented. Applications are made to attractivity, convergence, strong repellors, uniform persistence, and permanence. A result of Schreiber on robust permanence is improved.

Original language	English (US)
Pages (from-to)	107-131
Number of pages	25
Journal	Journal of Dynamics and Differential Equations
Volume	13
Issue number	1
DOIs	https://doi.org/10.1023/A:1009044515567
State	Published - 2001

Keywords

Asymptotic pseudo-orbits
Attractors
Chain transitive sets
Robust permanence
Strong repellors
Uniform persistence

ASJC Scopus subject areas

Analysis

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10.1023/A:1009044515567

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title = "Chain transitivity, attractivity, and strong repellors for semidynamical systems",

abstract = "Some properties of internally chain transitive sets for continuous maps in metric spaces are presented. Applications are made to attractivity, convergence, strong repellors, uniform persistence, and permanence. A result of Schreiber on robust permanence is improved.",

keywords = "Asymptotic pseudo-orbits, Attractors, Chain transitive sets, Robust permanence, Strong repellors, Uniform persistence",

author = "Hirsch, {Morris W.} and Hal Smith and Zhao, {Xiao Qiang}",

note = "Funding Information: M.W.H. was supported by NSF Grant DMS 9802182. X.-Q.Z. was supported by NSF Grant DMS 9700910.",

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T1 - Chain transitivity, attractivity, and strong repellors for semidynamical systems

AU - Hirsch, Morris W.

AU - Smith, Hal

AU - Zhao, Xiao Qiang

N1 - Funding Information: M.W.H. was supported by NSF Grant DMS 9802182. X.-Q.Z. was supported by NSF Grant DMS 9700910.

PY - 2001

Y1 - 2001

N2 - Some properties of internally chain transitive sets for continuous maps in metric spaces are presented. Applications are made to attractivity, convergence, strong repellors, uniform persistence, and permanence. A result of Schreiber on robust permanence is improved.

AB - Some properties of internally chain transitive sets for continuous maps in metric spaces are presented. Applications are made to attractivity, convergence, strong repellors, uniform persistence, and permanence. A result of Schreiber on robust permanence is improved.

KW - Asymptotic pseudo-orbits

KW - Attractors

KW - Chain transitive sets

KW - Robust permanence

KW - Strong repellors

KW - Uniform persistence

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IS - 1

ER -

Chain transitivity, attractivity, and strong repellors for semidynamical systems

Abstract

Keywords

ASJC Scopus subject areas

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