Polynomial convergence rate at infinity for the cusp winding spectrum of generalized Schottky groups
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918289392795648 |
|---|---|
| author | Arima, Yuya |
| author_facet | Arima, Yuya |
| contents | We show that the convergence rate of the cusp winding spectrum to the Hausdorff dimension of the limit set of a generalized Schottky group with one parabolic generator is polynomial. Our main theorem provides the new phenomenon in which differences in the Hausdorff dimension of the limit set generated by a Markov system cause essentially different results on multifractal analysis. This paper also provides a new characterization of the geodesic flow on the Poincaŕe disc model of two-dimensional hyperbolic space and the limit set of a generalized Schottky group. To prove our main theorem we use thermodynamic formalism on a countable Markov shift, gamma function, and zeta function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12398 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polynomial convergence rate at infinity for the cusp winding spectrum of generalized Schottky groups Arima, Yuya Dynamical Systems We show that the convergence rate of the cusp winding spectrum to the Hausdorff dimension of the limit set of a generalized Schottky group with one parabolic generator is polynomial. Our main theorem provides the new phenomenon in which differences in the Hausdorff dimension of the limit set generated by a Markov system cause essentially different results on multifractal analysis. This paper also provides a new characterization of the geodesic flow on the Poincaŕe disc model of two-dimensional hyperbolic space and the limit set of a generalized Schottky group. To prove our main theorem we use thermodynamic formalism on a countable Markov shift, gamma function, and zeta function. |
| title | Polynomial convergence rate at infinity for the cusp winding spectrum of generalized Schottky groups |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2407.12398 |