Dynamics on fences
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908947758186496 |
|---|---|
| author | Činč, Jernej Darji, Udayan B. Vejnar, Benjamin |
| author_facet | Činč, Jernej Darji, Udayan B. Vejnar, Benjamin |
| contents | Homeomorphisms of the Cantor set play a central role in topology, dynamical systems and descriptive set theory. In parallel, several classes of fence-like spaces - such as the hairy Cantor set, hairy arcs, Cantor bouquets in complex dynamics, the Lelek fan in topology and Fraïssé fence in descriptive set theory - have recently been studied for their rich structural and dynamical properties. In this paper, we introduce a general construction that associates to each homeomorphism of the Cantor set a canonically defined homeomorphism of a corresponding fence space. This construction lifts dynamical properties from the Cantor set to these fence-like spaces, allowing one to systematically transfer features such as minimality, recurrence, and orbit structure. As a consequence, we obtain a unified framework for studying dynamics on a broad class of fence-like spaces and establish new connections between their topological structure and induced dynamical behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07088 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynamics on fences Činč, Jernej Darji, Udayan B. Vejnar, Benjamin Dynamical Systems General Topology 37B05, 37F10, 37B45, 03C15 Homeomorphisms of the Cantor set play a central role in topology, dynamical systems and descriptive set theory. In parallel, several classes of fence-like spaces - such as the hairy Cantor set, hairy arcs, Cantor bouquets in complex dynamics, the Lelek fan in topology and Fraïssé fence in descriptive set theory - have recently been studied for their rich structural and dynamical properties. In this paper, we introduce a general construction that associates to each homeomorphism of the Cantor set a canonically defined homeomorphism of a corresponding fence space. This construction lifts dynamical properties from the Cantor set to these fence-like spaces, allowing one to systematically transfer features such as minimality, recurrence, and orbit structure. As a consequence, we obtain a unified framework for studying dynamics on a broad class of fence-like spaces and establish new connections between their topological structure and induced dynamical behavior. |
| title | Dynamics on fences |
| topic | Dynamical Systems General Topology 37B05, 37F10, 37B45, 03C15 |
| url | https://arxiv.org/abs/2604.07088 |