Density of mode-locking property for quasi-periodically forced Arnold circle maps - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

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

Résumé

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}.

Dates et versions

hal-04255435 , version 1 (24-10-2023)

Identifiants

Citer

Jian Wang, Zhiyuan Zhang. Density of mode-locking property for quasi-periodically forced Arnold circle maps. 2023. ⟨hal-04255435⟩
21 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More