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Dynamical Systems
An International Journal
Volume 27, 2012 - Issue 1: Jaroslav Stark Memorial Issue
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Original Articles

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

Paul Glendinning Centre for Interdisciplinary Computational and Dynamical Analysis (CICADA), University of Manchester, Manchester M13 9PL, UK; School of Mathematics, University of Manchester, Manchester M13 9PL, UKCorrespondence[email protected]
&
Silvia Pina-Romero School of Mathematics, University of Manchester, Manchester M13 9PL, UK
Pages 45-56 | Received 16 Jun 2011, Accepted 30 Oct 2011, Published online: 22 Mar 2012
 
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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.

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