Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2511.01034 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912683389878272 |
|---|---|
| author | Bédaride, Nicolas Cassaigne, Julien Hubert, Pascal Leplaideur, Renaud |
| author_facet | Bédaride, Nicolas Cassaigne, Julien Hubert, Pascal Leplaideur, Renaud |
| contents | On the full shift on two symbols, we consider the potential defined by $V(x) = \frac{1}{n}$ where $n$ denotes the longest common prefix between the infinite word $x$ and an element of the subshift associated to the Thue-Morse substitution. Given a non negative real number $β$, the pressure function is $P(β):=\sup\left\{h_μ+β\int V\,dμ\right\},$ where the supremum is taken over all shift invariant probabilities $μ$ on the full shift and $h_μ$ is the Kolmogorov entropy. We prove that there is a freezing phase transition for the potential $V$: For $β$ large enough, the pressure $P(\be)$ is equal to zero. Similar results were previously published by Bruin and Leplaideur in \cite{BL2}, \cite{Bruin-Leplaid-13} but their proofs contained significant gaps and required substantial clarification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01034 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Freezing phase transition for the Thue-Morse subshift Bédaride, Nicolas Cassaigne, Julien Hubert, Pascal Leplaideur, Renaud Dynamical Systems On the full shift on two symbols, we consider the potential defined by $V(x) = \frac{1}{n}$ where $n$ denotes the longest common prefix between the infinite word $x$ and an element of the subshift associated to the Thue-Morse substitution. Given a non negative real number $β$, the pressure function is $P(β):=\sup\left\{h_μ+β\int V\,dμ\right\},$ where the supremum is taken over all shift invariant probabilities $μ$ on the full shift and $h_μ$ is the Kolmogorov entropy. We prove that there is a freezing phase transition for the potential $V$: For $β$ large enough, the pressure $P(\be)$ is equal to zero. Similar results were previously published by Bruin and Leplaideur in \cite{BL2}, \cite{Bruin-Leplaid-13} but their proofs contained significant gaps and required substantial clarification. |
| title | Freezing phase transition for the Thue-Morse subshift |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2511.01034 |