Density of mode-locking property for quasi-periodically forced Arnold circle maps
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929596850503680 |
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| author | Wang, Jian Zhang, Zhiyuan |
| author_facet | Wang, Jian Zhang, Zhiyuan |
| contents | We show that the mode-locking region of the family of quasi-periodically forced Arnold circle maps with a topologically generic forcing function is dense. This gives a rigorous verification of certain numerical observations in \cite{DGO} for such forcing functions. More generally, under some general conditions on the base map, we show the density of the mode-locking property among dynamically forced maps (defined in \cite{Zha}) equipped with a topology that is much stronger than the $C^0$ topology, compatible with smooth fiber maps. For quasi-periodic base maps, our result generalizes the main results in \cite{ABD, WZJ, Zha}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_02087 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Density of mode-locking property for quasi-periodically forced Arnold circle maps Wang, Jian Zhang, Zhiyuan Dynamical Systems Mathematical Physics We show that the mode-locking region of the family of quasi-periodically forced Arnold circle maps with a topologically generic forcing function is dense. This gives a rigorous verification of certain numerical observations in \cite{DGO} for such forcing functions. More generally, under some general conditions on the base map, we show the density of the mode-locking property among dynamically forced maps (defined in \cite{Zha}) equipped with a topology that is much stronger than the $C^0$ topology, compatible with smooth fiber maps. For quasi-periodic base maps, our result generalizes the main results in \cite{ABD, WZJ, Zha}. |
| title | Density of mode-locking property for quasi-periodically forced Arnold circle maps |
| topic | Dynamical Systems Mathematical Physics |
| url | https://arxiv.org/abs/2209.02087 |