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STABILITY OF PERIODIC-SOLUTIONS NEAR A COLLISION OF EIGENVALUES OF OPPOSITE SIGNATURE
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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 0305-0041.
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Abstract
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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | ||||
Publisher: | CAMBRIDGE UNIV PRESS | ||||
ISSN: | 0305-0041 | ||||
Official Date: | March 1991 | ||||
Dates: |
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Volume: | 109 | ||||
Number: | Part 2 | ||||
Number of Pages: | 29 | ||||
Page Range: | pp. 375-403 | ||||
Publication Status: | Published |
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