A characterization of ω-limit sets for piecewise monotone maps of the interval

• Autorzy: Andrew D. Barwell
• Języki publikacji: EN

Abstrakty

EN

For a piecewise monotone map f on a compact interval I, we characterize the ω-limit sets that are bounded away from the post-critical points of f. If the pre-critical points of f are dense, for example when f is locally eventually onto, and Λ ⊂ I is closed, invariant and contains no post-critical point, then Λ is the ω-limit set of a point in I if and only if Λ is internally chain transitive in the sense of Hirsch, Smith and Zhao; the proof relies upon symbolic dynamics. By identifying points of ω-limit sets via their limit-itineraries, we offer simple examples which show that internal chain transitivity does not characterize ω-limit sets for interval maps in general.

Kategorie tematyczne

• 54H20: Topological dynamics
• 54C05: Continuous maps
• 37B10: Symbolic dynamics
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 207
• Numer: 2
• Strony: 161-174

Daty

wydano

2010

Twórcy

autor

Andrew D. Barwell

• School of Mathematics and Statistics, University of Birmingham, Birmingham, B15 2TT, UK

Identyfikatory

DOI

10.4064/fm207-2-4