Quasiperiodicity in Dissipative Systems: A Renormalization Group Analysis

TitleQuasiperiodicity in Dissipative Systems: A Renormalization Group Analysis
Publication TypeJournal Article
Year of Publication1982
AuthorsFeigenbaum, M. J., Kadanoff L. P., & Shenker S.
Published inPhysica D: Nonlinear Phenomena
Volume5
Issue2-3
Page(s)370-386
Other Numbers3492
Abstract

Dynamical systems with quasiperiodic behavior, i.e., two incommensurate frequencies, may be studied via discrete maps which show smooth continuous invariant curves with irrational winding number. In this paper these curves are followed using renormalization group techniques which are applied to a one-dimensional system (circle) and also to an area-contracting map of an annulus. Two fixed points are found representing different types of universal behavior: a trivial fixed point for smooth motion and a nontrivial fixed point. The latter representsthe incipient breakup of a quasiperiodic motion with frequency ratio the golden mean into a more chaotic flow. Fixed point functions are determined numerically and via an ?-expansion and eigenvalues are calculated.

Bibliographic Notes

Physica D: Nonlinear Phenomena, Vol. 5, Issue 2-3, pp. 370-386

Abbreviated Authors

M. J. Feigenbaum, L. P. Kadanoff, and S. Shenker

ICSI Research Group

Networking and Security

ICSI Publication Type

Article in journal or magazine