Stability-instability transitions in Hamiltonian systems of n dimensions

Authors

Foek T. Hioe, Saint John Fisher UniversityFollow
Z Deng

Document Type

Article

Publication Date

1-15-1987

Abstract

We show analytically that for a class of simple periodic motions in a general Hamiltonian system of n dimensions, if C is a parameter of the system and Cz one of its generally many critical values at which the motion undergoes a stability-instability transition, the behavior of the largest Lyapunov exponent p as C approaches Ce from the unstable region is given by µ, =constX |~ C—C_p |^β where β= 1/2, independent of the transition point, type of transitions, or the dimensionality of the system. We present numerical results for a three-dimensional Harniltonian system which exhibits three types of stability-instability transitions, and for a two-dimensional Hamiltonian system which exhibits two types of transitions.

DOI

10.1103/PhysRevA.35.847

Comments

©1987, The American Physical Society. Original publication is available at

http://link.aps.org/doi/10.1103/PhysRevA.36.724

Publication Information

Hioe, Foek T. and Deng, Z (1987). "Stability-instability transitions in Hamiltonian systems of n dimensions." Physical Review A 35.2, 847-856.

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