Shadowing and internal chain transitivity

Jonathan Meddaugh, and Brian E. Raines. "Shadowing and internal chain transitivity." Fundamenta Mathematicae 222.3 (2013): 279-287. <http://eudml.org/doc/283347>.

@article{JonathanMeddaugh2013,
abstract = {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.},
author = {Jonathan Meddaugh, Brian E. Raines},
journal = {Fundamenta Mathematicae},
keywords = {omega-limit set; shadowing; internal chain transitivity; space of omega-limit sets},
language = {eng},
number = {3},
pages = {279-287},
title = {Shadowing and internal chain transitivity},
url = {http://eudml.org/doc/283347},
volume = {222},
year = {2013},
}

TY - JOUR
AU - Jonathan Meddaugh
AU - Brian E. Raines
TI - Shadowing and internal chain transitivity
JO - Fundamenta Mathematicae
PY - 2013
VL - 222
IS - 3
SP - 279
EP - 287
AB - 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.
LA - eng
KW - omega-limit set; shadowing; internal chain transitivity; space of omega-limit sets
UR - http://eudml.org/doc/283347
ER -