Refinement of Bratteli-Vershik models
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2020
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916075583569920 |
|---|---|
| author | Shimomura, Takashi |
| author_facet | Shimomura, Takashi |
| contents | In the zero-dimensional systems, the Bratteli-Vershik models can be built upon certain closed sets that are called `quasi-sections' in this article. There exists a bijective correspondence between the topological conjugacy classes of triples of zero-dimensional systems and quasi-sections and the topological conjugacy classes of Bratteli-Vershik models. Therefore, we can get refined Bratteli-Vershik models if we get certain refined quasi-sections. The basic sets are such refined quasi-sections that bring `closing property' on the corresponding Bratteli-Vershik models. We show a direct proof on the existence of basic sets. Thorough investigations on quasi-sections and basic sets are done. Furthermore, it would be convenient for the Bratteli-Vershik models to concern minimal sets. To this point, we show the existence of the Bratteli-Vershik models whose minimal sets are properly ordered. On the other hand, we can get certain refinements with respect to the Bratteli-Vershikizability condition or the decisiveness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_02617 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Refinement of Bratteli-Vershik models Shimomura, Takashi Dynamical Systems Primary 37B05, 37B10 In the zero-dimensional systems, the Bratteli-Vershik models can be built upon certain closed sets that are called `quasi-sections' in this article. There exists a bijective correspondence between the topological conjugacy classes of triples of zero-dimensional systems and quasi-sections and the topological conjugacy classes of Bratteli-Vershik models. Therefore, we can get refined Bratteli-Vershik models if we get certain refined quasi-sections. The basic sets are such refined quasi-sections that bring `closing property' on the corresponding Bratteli-Vershik models. We show a direct proof on the existence of basic sets. Thorough investigations on quasi-sections and basic sets are done. Furthermore, it would be convenient for the Bratteli-Vershik models to concern minimal sets. To this point, we show the existence of the Bratteli-Vershik models whose minimal sets are properly ordered. On the other hand, we can get certain refinements with respect to the Bratteli-Vershikizability condition or the decisiveness. |
| title | Refinement of Bratteli-Vershik models |
| topic | Dynamical Systems Primary 37B05, 37B10 |
| url | https://arxiv.org/abs/2010.02617 |