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arXiv · 1607.01700

Genericity of mode-locking for quasiperiodically forced circle maps

Jing Wang·Qi Zhou·Tobias Jäger
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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.

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Jing Wang, Qi Zhou, Tobias Jäger. 2017-01-08. Genericity of mode-locking for quasiperiodically forced circle maps. https://doi.org/10.1007/s00220-017-2870-5

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