Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)


Rotation numbers for quasiperiodically forced circle maps-mode-locking vs. strict monotonicity

Authors: Kristian Bjerklöv and Tobias Jäger
Journal: J. Amer. Math. Soc. 22 (2009), 353-362
MSC (2000): Primary 37E45, 37B55
Published electronically: October 21, 2008
MathSciNet review: 2476777
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We describe the relation between the dynamical properties of a quasiperiodically forced orientation-preserving circle homeomorphism $ f$ and the behaviour of the fibred rotation number with respect to strictly monotone perturbations. Despite the fact that the dynamics in the forced case can be considerably more complicated, the result we obtain is in perfect analogy with the one-dimensional situation. In particular, the fibred rotation number behaves strictly monotonically whenever the rotation vector of $ f$ is irrational, which answers a question posed by Herman (1983). In addition, we obtain the continuous structure of the Arnold tongues in parameter families such as the quasiperiodically forced Arnold circle map.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 37E45, 37B55

Retrieve articles in all journals with MSC (2000): 37E45, 37B55

Additional Information

Kristian Bjerklöv
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G4

Tobias Jäger
Affiliation: Department of Mathematics, Collège de France, 3 rue d’Ulm, 75005 Paris, France

PII: S 0894-0347(08)00627-9
Keywords: Rotation numbers, mode-locking, quasiperiodically forced systems.
Received by editor(s): August 10, 2006
Published electronically: October 21, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia