Shadowing and internal chain transitivity

• Autorzy: Jonathan Meddaugh , Brian E. Raines
• Języki publikacji: EN

Abstrakty

EN

The main result of this paper is that a map f: X → X which has shadowing and for which the space of ω-limits sets is closed in the Hausdorff topology has the property that a set A ⊆ X is an ω-limit set if and only if it is closed and internally chain transitive. Moreover, a map which has the property that every closed internally chain transitive set is an ω-limit set must also have the property that the space of ω-limit sets is closed. As consequences of this result, we show that interval maps with shadowing have the property that every internally chain transitive set is an ω-limit set of a point, and we also show that topologically hyperbolic maps and certain quadratic Julia sets have a closed space of ω-limit sets.

Kategorie tematyczne

• 54H20: Topological dynamics
• 37B10: Symbolic dynamics
• 37B20: Notions of recurrence
• 37B50: Multi-dimensional shifts of finite type, tiling dynamics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 222
• Numer: 3
• Strony: 279-287

Daty

wydano

2013

Twórcy

autor

Jonathan Meddaugh

• Department of Mathematics, Baylor University, Waco, TX 76798-7328, U.S.A.

autor

Brian E. Raines

• Department of Mathematics, Baylor University, Waco, TX 76798-7328, U.S.A.

Identyfikatory

DOI

10.4064/fm222-3-4