Stability of periodic solutions near a collision of eigenvalues of opposite signature

Author:

Bridges Thomas J.

Abstract

AbstractSome general observations about stability of periodic solutions of Hamiltonian systems are presented as well as stability results for the periodic solutions that exist near a collision of pure imaginary eigenvalues. Let I = ∮ p dq be the action functional for a periodic orbit. The stability theory is based on the surprising result that changes in stability are associated with changes in the sign of dI / dw, where w is the frequency of the periodic orbit. A stability index based on dI / dw is defined and rigorously justified using Floquet theory and complete results for the stability (and instability) of periodic solutions near a collision of pure imaginary eigenvalues of opposite signature (the 1: – 1 resonance) are obtained.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference12 articles.

1. [11] Poincaré H. . Les Méthodes Nouvelles de la Méchanique Céleste (NASA Translation TT/F–450–452, 1967).

2. The Hamiltonian Hopf Bifurcation

3. Nonsemisimple 1?1 resonance at an equilibrium

4. Singularities and Groups in Bifurcation Theory

5. Nonlinear Functional Analysis

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