Forcing among exact patterns of triods
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909936361930752 |
|---|---|
| author | Bhattacharya, Sourav |
| author_facet | Bhattacharya, Sourav |
| contents | We obtain a complete characterization of \emph{topologically exact patterns} on \emph{triods}. Based on their \emph{rotation number} $ρ$, these \emph{exact patterns} are grouped into three classes: \emph{slow} ($ρ< \frac{1}{3}$), \emph{fast} ($ρ> \frac{1}{3}$) and \emph{ternary} ($ρ= \frac{1}{3}$). For each category, we derive a \emph{linear ordering} of the set of natural numbers, $\mathbb{N}$ that captures \emph{forcing} between the \emph{patterns}. We also show that each of these orderings is \emph{stable} under perturbations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Forcing among exact patterns of triods Bhattacharya, Sourav Dynamical Systems Primary 37E05, 37E15, 37E25, 37E40, Secondary 37E45 37B20 We obtain a complete characterization of \emph{topologically exact patterns} on \emph{triods}. Based on their \emph{rotation number} $ρ$, these \emph{exact patterns} are grouped into three classes: \emph{slow} ($ρ< \frac{1}{3}$), \emph{fast} ($ρ> \frac{1}{3}$) and \emph{ternary} ($ρ= \frac{1}{3}$). For each category, we derive a \emph{linear ordering} of the set of natural numbers, $\mathbb{N}$ that captures \emph{forcing} between the \emph{patterns}. We also show that each of these orderings is \emph{stable} under perturbations. |
| title | Forcing among exact patterns of triods |
| topic | Dynamical Systems Primary 37E05, 37E15, 37E25, 37E40, Secondary 37E45 37B20 |
| url | https://arxiv.org/abs/2510.04155 |