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

Fundamenta Mathematicae (2010)

- Volume: 207, Issue: 2, page 161-174
- ISSN: 0016-2736

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topAndrew D. Barwell. "A characterization of ω-limit sets for piecewise monotone maps of the interval." Fundamenta Mathematicae 207.2 (2010): 161-174. <http://eudml.org/doc/283314>.

@article{AndrewD2010,

abstract = {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.},

author = {Andrew D. Barwell},

journal = {Fundamenta Mathematicae},

keywords = {omega-limit set; piecewise monotone map; symbolic dynamics; kneading theory},

language = {eng},

number = {2},

pages = {161-174},

title = {A characterization of ω-limit sets for piecewise monotone maps of the interval},

url = {http://eudml.org/doc/283314},

volume = {207},

year = {2010},

}

TY - JOUR

AU - Andrew D. Barwell

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

JO - Fundamenta Mathematicae

PY - 2010

VL - 207

IS - 2

SP - 161

EP - 174

AB - 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.

LA - eng

KW - omega-limit set; piecewise monotone map; symbolic dynamics; kneading theory

UR - http://eudml.org/doc/283314

ER -

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