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
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
Publisher:	CAMBRIDGE UNIV PRESS
ISSN:	0305-0041
Date:	March 1991
Volume:	109
Number:	Part 2
Number of Pages:	29
Page Range:	pp. 375-403
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/22785

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