Products of exact dynamical systems and Lorentzian continued fractions
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910972890841088 |
|---|---|
| author | Barreto-Rosa, Brandon G. Burelle, Jean-Philippe Lukyanenko, Anton Richey, Martha |
| author_facet | Barreto-Rosa, Brandon G. Burelle, Jean-Philippe Lukyanenko, Anton Richey, Martha |
| contents | We describe a new continued fraction system in Minkowski space $\mathbb R^{1,1}$, proving convergence, ergodicity with respect to an explicit invariant measure, and Lagrange's theorem. The proof of ergodicity leads us to the question of exactness for products of dynamical systems. Under technical assumptions, namely Renyi's condition, we show that products of exact dynamical systems are again exact, allowing us to study $α$-type perturbations of the system. In addition, we describe new CF systems in $\mathbb R^{1,1}$ and $\mathbb R^{2,1}\cong \mathrm{Sym}_2(\mathbb R)$ that, based on experimental evidence, we conjecture to be convergent and ergodic with respect to a finite invariant measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22556 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Products of exact dynamical systems and Lorentzian continued fractions Barreto-Rosa, Brandon G. Burelle, Jean-Philippe Lukyanenko, Anton Richey, Martha Dynamical Systems Number Theory 37A44, 11K50 We describe a new continued fraction system in Minkowski space $\mathbb R^{1,1}$, proving convergence, ergodicity with respect to an explicit invariant measure, and Lagrange's theorem. The proof of ergodicity leads us to the question of exactness for products of dynamical systems. Under technical assumptions, namely Renyi's condition, we show that products of exact dynamical systems are again exact, allowing us to study $α$-type perturbations of the system. In addition, we describe new CF systems in $\mathbb R^{1,1}$ and $\mathbb R^{2,1}\cong \mathrm{Sym}_2(\mathbb R)$ that, based on experimental evidence, we conjecture to be convergent and ergodic with respect to a finite invariant measure. |
| title | Products of exact dynamical systems and Lorentzian continued fractions |
| topic | Dynamical Systems Number Theory 37A44, 11K50 |
| url | https://arxiv.org/abs/2505.22556 |