Topological Sequence Entropy of co-Induced Systems
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911211416715264 |
|---|---|
| author | Leonard, Dakota M. |
| author_facet | Leonard, Dakota M. |
| contents | Let $G$ be a discrete, countably infinite group and $H$ a subgroup of $G$. If $H$ acts continuously on a compact metric space $X$, then we can induce a continuous action of $G$ on $\prod_{H\backslash G}X$ where $H\backslash G$ is the collection of right-cosets of $H$ in $G$. This process is known as the co-induction. In this article, we will calculate the maximal pattern entropy of the co-induction. If $[G:H] < +\infty$ we will show that the $H$ action is null if and only if the co-induced action of $G$ is null. Also, we will discuss an example where $H$ is a proper subgroup of $G$ with finite index where the maximal pattern entropy of the $H$ action is equal to the co-induced action of $G$. If $[G:H] = +\infty$ we will show that the maximal pattern entropy of the co-induction is always $+\infty$ given the $H$-system is not trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10745 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological Sequence Entropy of co-Induced Systems Leonard, Dakota M. Dynamical Systems Let $G$ be a discrete, countably infinite group and $H$ a subgroup of $G$. If $H$ acts continuously on a compact metric space $X$, then we can induce a continuous action of $G$ on $\prod_{H\backslash G}X$ where $H\backslash G$ is the collection of right-cosets of $H$ in $G$. This process is known as the co-induction. In this article, we will calculate the maximal pattern entropy of the co-induction. If $[G:H] < +\infty$ we will show that the $H$ action is null if and only if the co-induced action of $G$ is null. Also, we will discuss an example where $H$ is a proper subgroup of $G$ with finite index where the maximal pattern entropy of the $H$ action is equal to the co-induced action of $G$. If $[G:H] = +\infty$ we will show that the maximal pattern entropy of the co-induction is always $+\infty$ given the $H$-system is not trivial. |
| title | Topological Sequence Entropy of co-Induced Systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2409.10745 |