Genericity of mode-locking for quasiperiodically forced circle maps
Dynamical Systems
2017-04-26 v2
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.
Keywords
Cite
@article{arxiv.1607.01700,
title = {Genericity of mode-locking for quasiperiodically forced circle maps},
author = {Jing Wang and Qi Zhou and Tobias Jäger},
journal= {arXiv preprint arXiv:1607.01700},
year = {2017}
}
Comments
17 pages,2 figures