Authomorphic measures with negative exponents for multicritical circle maps
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912290831335424 |
|---|---|
| author | Goncharuk, Nataliya Yampolsky, Michael |
| author_facet | Goncharuk, Nataliya Yampolsky, Michael |
| contents | Authomorphic or $s$-measures for circle diffeomorphisms were introduced by R.Douady and J.-C. Yoccoz in 1999. They have multiple applications in circle dynamics, with the case $s=-1$ being particularly important for describing conjugacy classes. In arxiv:2306.13524, E. de Faria, P. Guarino and B. Nussenzveig proved existence and uniqueness of automorphic $s$-measures for multicritical circle maps for all $s>0$. The purpose of this paper is to extend these results to $s$-measures with negative values of $s$. As an application, we prove a smoothness result for irrational Arnold tongues in families of multicritical maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03780 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Authomorphic measures with negative exponents for multicritical circle maps Goncharuk, Nataliya Yampolsky, Michael Dynamical Systems 37E10, 37E45 Authomorphic or $s$-measures for circle diffeomorphisms were introduced by R.Douady and J.-C. Yoccoz in 1999. They have multiple applications in circle dynamics, with the case $s=-1$ being particularly important for describing conjugacy classes. In arxiv:2306.13524, E. de Faria, P. Guarino and B. Nussenzveig proved existence and uniqueness of automorphic $s$-measures for multicritical circle maps for all $s>0$. The purpose of this paper is to extend these results to $s$-measures with negative values of $s$. As an application, we prove a smoothness result for irrational Arnold tongues in families of multicritical maps. |
| title | Authomorphic measures with negative exponents for multicritical circle maps |
| topic | Dynamical Systems 37E10, 37E45 |
| url | https://arxiv.org/abs/2404.03780 |