A note on actions with finite orbits on dendrites
| Autor: | Abdalaoui, el Houcein el, Naghmouchi, Issam |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | It is shown that the restriction of the action of any group with finite orbit on the minimal sets of dendrites is equicontinuous. Consequently, we obtain that the action of any amenable group and Thompson group on dendrite restricted on minimal sets is equicontinuous. We further provide a class of non-amenable groups whose action on dendrites has finite orbit. We extend also some of our results to dendron. We further give a characterization of the set of invariant probability measures and its extreme points. Comment: 20 pages. This new version is augmented and revised. We add a new results. The strategy to tackle the problem of amenability of Thompson group is highlighted using the result of Glasner which say that the locally compact group is amenable iff it has no nontrivial strongly proximal flow |
| Databáze: | arXiv |
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