Density of mode-locking property for quasi-periodically forced Arnold circle maps

Fuente: arXiv
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Auteurs principaux: Wang, Jian, Zhang, Zhiyuan
Format: Preprint
Publié: 2022
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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