Characterizations of ω-Limit Sets of Topologically Hyperbolic Systems
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2011
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| _version_ | 1866913117340958720 |
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| author | Barwell, Andrew Good, Chris Oprocha, Piotr Raines, Brian |
| author_facet | Barwell, Andrew Good, Chris Oprocha, Piotr Raines, Brian |
| contents | 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 ω-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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1111_0765 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Characterizations of ω-Limit Sets of Topologically Hyperbolic Systems Barwell, Andrew Good, Chris Oprocha, Piotr Raines, Brian Dynamical Systems 54H20 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 ω-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. |
| title | Characterizations of ω-Limit Sets of Topologically Hyperbolic Systems |
| topic | Dynamical Systems 54H20 |
| url | https://arxiv.org/abs/1111.0765 |