تقرير
Local $\mathcal{P}$ entropy and stabilized automorphism groups of subshifts
| العنوان: | Local $\mathcal{P}$ entropy and stabilized automorphism groups of subshifts |
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| المؤلفون: | Schmieding, Scott |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems, 37B10 |
| الوصف: | For a homeomorphism $T \colon X \to X$ of a compact metric space $X$, the stabilized automorphism group $\text{Aut}^{(\infty)}(T)$ consists of all self-homeomorphisms of $X$ which commute with some power of $T$. Motivated by the study of these groups in the context of shifts of finite type, we introduce a certain entropy for groups called local $\mathcal{P}$ entropy. We show that when $(X,T)$ is a non-trivial mixing shift of finite type, the local $\mathcal{P}$ entropy of the group $\text{Aut}^{(\infty)}(T)$ is determined by the topological entropy of $(X,T)$. We use this to give a complete classification of the isomorphism type of the stabilized automorphism groups of full shifts. Comment: 29 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2007.02183 |
| رقم الأكسشن: | edsarx.2007.02183 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |