Genericity of mode-locking for quasiperiodically forced circle maps

Abstract

We show that a generic quasiperiodically forced circle homeomorphism is mode-locked: the rotation number in the fibres is rationally related to the rotation number in the base and it is stable under small perturbations of the system. As a consequence, this implies that for a generic parameter family of quasiperiodically forced circle homeomorphisms satisfying a twist condition, the graph of the rotation number as a function of the parameter is a devil's staircase.

arXiv comment17 pages,2 figures

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Cited by in corpus (5)

• Linearization of quasiperiodically forced circle flow beyond Brjuno condition
• On topological genericity of the mode-locking phenomenon
• Density of mode-locking property for quasi-periodically forced Arnold circle maps
• Quantitative almost reducibility and Möbius disjointness for analytic quasiperiodic Schrodinger cocycles
• Rectifiability of a class of invariant measures with one non-vanishing Lyapunov exponent