STABILITY OF PERIODIC-SOLUTIONS NEAR A COLLISION OF EIGENVALUES OF OPPOSITE SIGNATURE
UNSPECIFIED. (1991) STABILITY OF PERIODIC-SOLUTIONS NEAR A COLLISION OF EIGENVALUES OF OPPOSITE SIGNATURE. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 109 (Part 2). pp. 375-403. ISSN 0305-0041Full text not available from this repository.
Some 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 = closed-intergral pdq 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/d-omega, where omega is the frequency of the periodic orbit. A stability index based on dI/d-omega 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.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY|
|Publisher:||CAMBRIDGE UNIV PRESS|
|Number of Pages:||29|
|Page Range:||pp. 375-403|
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