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

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}.

arXiv commentMinor corrections are made

References in corpus (5)

• Genericity of zero Lyapunov exponents
• Some Characterizations of Domination
• Cantor Spectrum for Schrödinger Operators with Potentials arising from Generalized Skew-shifts
• Linearization of quasiperiodically forced circle flow beyond Brjuno condition
• Genericity of mode-locking for quasiperiodically forced circle maps