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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2412.08884 |
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| _version_ | 1866912153428033536 |
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| author | Radić, Tristán |
| author_facet | Radić, Tristán |
| contents | Partial rigidity is a quantitative notion of recurrence and provides a global obstruction which prevents the system from being strongly mixing. A dynamical system $(X, \mathcal{X}, μ, T)$ is partially rigid if there is a constant $δ>0$ and sequence $(n_k)_{k \in \mathbb{N}}$ such that $\displaystyle \liminf_{k \to \infty } μ(A \cap T^{n_k}A) \geq δμ(A)$ for every $A \in \mathcal{X}$, and the partial rigidity rate is the largest $δ$ achieved over all sequences. For every integer $d \geq 1$, via an explicit construction, we prove the existence of a minimal subshift $(X,S)$ with $d$ ergodic measures having distinct partial rigidity rates. The systems built are $\mathcal{S}$-adic subshifts of finite alphabetic rank that have non-superlinear word complexity and, in particular, have zero entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08884 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiple partial rigidity rates in low complexity subshifts Radić, Tristán Dynamical Systems 37A05, 37B10 Partial rigidity is a quantitative notion of recurrence and provides a global obstruction which prevents the system from being strongly mixing. A dynamical system $(X, \mathcal{X}, μ, T)$ is partially rigid if there is a constant $δ>0$ and sequence $(n_k)_{k \in \mathbb{N}}$ such that $\displaystyle \liminf_{k \to \infty } μ(A \cap T^{n_k}A) \geq δμ(A)$ for every $A \in \mathcal{X}$, and the partial rigidity rate is the largest $δ$ achieved over all sequences. For every integer $d \geq 1$, via an explicit construction, we prove the existence of a minimal subshift $(X,S)$ with $d$ ergodic measures having distinct partial rigidity rates. The systems built are $\mathcal{S}$-adic subshifts of finite alphabetic rank that have non-superlinear word complexity and, in particular, have zero entropy. |
| title | Multiple partial rigidity rates in low complexity subshifts |
| topic | Dynamical Systems 37A05, 37B10 |
| url | https://arxiv.org/abs/2412.08884 |