Group action on local dendrites
| Autor: | Aymen Haj Salem, Hawete Hattab |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pointwise
Group (mathematics) 010102 general mathematics 01 natural sciences Combinatorics Cantor set Flow (mathematics) Cover (topology) 0103 physical sciences Dendrite (mathematics) Countable set 010307 mathematical physics Geometry and Topology Finitely generated group 0101 mathematics Mathematics |
| Zdroj: | Topology and its Applications. 247:91-99 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2018.08.002 |
| Popis: | Let G be a group acting by homeomorphisms on a local dendrite X with countable set of endpoints. In this paper, it is shown that any minimal set M of G is either a finite orbit, or a Cantor set or a circle. Furthermore, we prove that if G is a finitely generated group, then the flow ( G , X ) is a pointwise recurrent flow if and only if one of the following two statements holds: (1) X = S 1 , and ( G , S 1 ) is a minimal flow conjugate to an isometric flow, or to a finite cover of a proximal flow; (2) ( G , X ) is pointwise periodic. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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