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Invariant measures of Toeplitz subshifts on non-amenable groups
- Publication Year :
- 2023
-
Abstract
- Let $G$ be a countable residually finite group (for instance $\mathbb{F}_2$) and let $\overleftarrow{G}$ be a totally disconnected metric compactification of $G$ equipped with the action of $G$ by left multiplication. For every $r\geq 1$ we construct a Toeplitz $G$-subshift $(X,\sigma,G)$, which is an almost one-to-one extension of $\overleftarrow{G}$, having $r$ ergodic measures $\nu_1, \cdots,\nu_r$ such that for every $1\leq i\leq r$ the measure-theoretic dynamical system $(X,\sigma,G,\nu_i)$ is isomorphic to $\overleftarrow{G}$ endowed with the Haar measure. The construction we propose is general (for amenable and non-amenable residually finite groups), however, we point out the differences and obstructions that could appear when the acting group is not amenable.<br />Comment: 29 pages
- Subjects :
- Mathematics - Dynamical Systems
37B05, 37B10
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2305.09835
- Document Type :
- Working Paper