Characterizations of ω-limit sets in topologically hyperbolic systems

A.D. Barwell, C. Good, P. Oprocha, B.E. Raines

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


It is well known that ω-limit sets are internally chain transitive and have weak incompressibility; the converse is not generally true, in either case. However, it has been shown that a set is weakly incompressible if and only if it is an abstract !-limit set, and separately that in shifts of finite type, a set is internally chain transitive if and only if it is a (regular) ω-limit set. In this paper we generalise these and other results, proving that the characterization for shifts of finite type holds in a variety of topologically hyperbolic systems (defined in terms of expansive and shadowing properties), and also show that the notions of internal chain transitivity and weak incompressibility coincide in compact metric spaces.
Original languageEnglish
Pages (from-to)1819-1833
Number of pages15
JournalDiscrete and Continuous Dynamical Systems
Issue number5
Publication statusPublished - 1 May 2013


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