Quasiperiodicity in Dissipative Systems: A Renormalization Group Analysis
| Title | Quasiperiodicity in Dissipative Systems: A Renormalization Group Analysis |
| Publication Type | Journal Article |
| Year of Publication | 1982 |
| Authors | Feigenbaum, M. J., Kadanoff L. P., & Shenker S. |
| Published in | Physica D: Nonlinear Phenomena |
| Volume | 5 |
| Issue | 2-3 |
| Page(s) | 370-386 |
| Other Numbers | 3492 |
| 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 |