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arXiv · 2209.02087

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

Jian Wang·Zhiyuan Zhang
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Abstract

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}.

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Jian Wang, Zhiyuan Zhang. 2022-09-05. Density of mode-locking property for quasi-periodically forced Arnold circle maps. https://doi.org/10.1017/etds.2024.27

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