Universal scaling of rotation intervals for quasi-periodically forced circle maps

Abstract

We introduce a simplifying assumption which makes it possible to approximate the rotation number of an invertible quasi-periodically forced circle map by an integral in the limit of large forcing. We use this to describe universal scaling laws for the width of the non-trivial rotation interval of non-invertible quasi-periodically forced circle maps in this limit, and compare the results with numerical simulations.

Acknowledgements

P. Glendinning is partially funded by EPSRC grant EP/E050441/1. S. Prina-Romero is grateful to the University of Manchester and CONACYT.