RUELLES ROTATION FREQUENCY FOR A SYMPLECTIC CHAIN OF DISSIPATIVE OSCILLATORS

被引：8

作者：

DRESSLER, U ^{[1
]}

LAUTERBORN, W ^{[1
]}

机构：

[1] TH DARMSTADT, INST ANGEW PHYS, W-6100 DARMSTADT, GERMANY

来源：

PHYSICAL REVIEW A | 1990年 / 41卷 / 12期

关键词：

D O I：

10.1103/PhysRevA.41.6702

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

We present the calculation of Ruelles rotation number (frequency) for a chain of damped and driven coupled Duffing oscillators using the recently discovered symplectic structure of the system. A relation between the eigenvalues of periodic orbits and the winding number / is conjectured by making use of their Krein signatures. The occurrence and nonoccurrence of plateaus with respect to the driving frequency can be explained via this relation. © 1990 The American Physical Society.

引用

页码：6702 / 6715

页数：14

共 23 条

[1]

[Anonymous], 1978, MATH METHODS CLASSIC, DOI [DOI 10.1007/978-1-4757-1693-1, 10.1007/978-1-4757-1693-1]

[2] TOPOLOGY OF THE INVARIANT-MANIFOLDS OF PERIOD-DOUBLING ATTRACTORS FOR SOME FORCED NON-LINEAR OSCILLATORS [J].

BEIERSDORFER, P ;

WERSINGER, JM ;

TREVE, Y .

PHYSICS LETTERS A, 1983, 96 (06) :269-272

[3] UNIVERSALITY OF THE TOPOLOGY OF PERIOD DOUBLING DYNAMICAL-SYSTEMS [J].

BEIERSDORFER, P .

PHYSICS LETTERS A, 1984, 100 (08) :379-382

[4] SYMMETRY PROPERTY OF THE LYAPUNOV SPECTRA OF A CLASS OF DISSIPATIVE DYNAMICAL-SYSTEMS WITH VISCOUS DAMPING [J].

DRESSLER, U .

PHYSICAL REVIEW A, 1988, 38 (04) :2103-2109

[5] ERGODIC-THEORY OF CHAOS AND STRANGE ATTRACTORS [J].

ECKMANN, JP ;

RUELLE, D .

REVIEWS OF MODERN PHYSICS, 1985, 57 (03) :617-656

[6] THE NONLINEAR DYNAMICS OF THE DAMPED AND DRIVEN TODA CHAIN .1. ENERGY BIFURCATION DIAGRAMS [J].

GEIST, K ;

LAUTERBORN, W .

PHYSICA D, 1988, 31 (01) :103-116

[7]

GEIST K, 1989, THESIS U GOTTINGEN

[8]

GEIST K, IN PRESS PROGR THEOR

[9]

Goldstein H., 1980, CLASSICAL MECH, V2nd ed

[10]

Guckenheimer J., 2013, APPL MATH SCI, DOI 10.1007/978-1-4612- 1140-2

← 1 2 3 →