Homeomorphisms of Locally Finite Graphs

Hattab, Hawete; Salhi, Ezzeddine

doi:10.1007/s12346-015-0182-8

Cited by 1 publication

(3 citation statements)

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Section: Almost Periodicity Orbit Closure Relation and Orbit Spacementioning

confidence: 68%

“…(1) Corollary 5.6 extends Theorem 1.2 in [13]. Notice that if X is a graph different from a circle, Hattab [13] proved precisely that (G, X) is pointwise almost periodic if and only if G is finite. (2) If X is a circle, it is clear that if G is the group generated by an irrational rotation, then (G, X) is minimal but not pointwise periodic.…”

Section: Almost Periodicity Orbit Closure Relation and Orbit Spacementioning

confidence: 73%

“…For a single homeomorphism, Jmel [15] (resp. Hattab and Salhi [13]) has shown that if f is a pointwise periodic homeomorphism of X which is a dendrite (resp. a graph), then the orbit space X/f is Hausdorff.…”

Section: Remarkmentioning

confidence: 99%

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Minimal sets and orbit spaces for group actions on local dendrites

Marzougui

Naghmouchi

2018

Math. Z.

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We consider a group G acting on a local dendrite X (in particular on a graph). We give a full characterization of minimal sets of G by showing that any minimal set M of G (whenever X is different from a dendrite) is either a finite orbit, or a Cantor set, or a circle. If X is a graph different from a circle, such a minimal M is a finite orbit. These results extend those of the authors for group actions on dendrites. On the other hand, we show that, for any group G acting on a local dendrite X different from a circle, the following properties are equivalent: (1) (G, X) is pointwise almost periodic.(2) The orbit closure relation R = {(x, y) ∈ X × X : y ∈ G(x)} is closed. (3) Every non-endpoint of X is periodic. In addition, if G is countable and X is a local dendrite, then (G, X) is pointwise periodic if and only if the orbit space X/G is Hausdorff.

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Section: Almost Periodicity Orbit Closure Relation and Orbit Spacementioning

confidence: 68%

Section: Almost Periodicity Orbit Closure Relation and Orbit Spacementioning

confidence: 73%