Genericity of mode-locking for quasiperiodically forced circle maps
arXiv:1607.01700 · doi:10.1007/s00220-017-2870-5
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.
17 pages,2 figures