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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Multi-bump orbits homoclinic to resonance bands


Authors: Tasso J. Kaper and Gregor Kovacic
Journal: Trans. Amer. Math. Soc. 348 (1996), 3835-3887
MSC (1991): Primary 34A26, 34A47, 34C35, 34C37, 34D15
MathSciNet review: 1329536
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Abstract: We establish the existence of several classes of multi-bump orbits homoclinic to resonance bands for completely-integrable Hamiltonian systems subject to small-amplitude Hamiltonian or dissipative perturbations. Each bump is a fast excursion away from the resonance band, and the bumps are interspersed with slow segments near the resonance band. The homoclinic orbits, which include multi-bump \v{S}ilnikov orbits, connect equilibria and periodic orbits in the resonance band. The main tools we use in the existence proofs are the exchange lemma with exponentially small error and the existence theory of orbits homoclinic to resonance bands which make only one fast excursion away from the resonance bands.


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Additional Information

Tasso J. Kaper
Affiliation: Department of Mathematics, Boston University, Boston, Massachusetts 02215
Email: tasso@math.bu.edu

Gregor Kovacic
Affiliation: Mathematical Sciences Department, Rensselaer Polytechnic Institute, Troy, New York 12180
Email: kovacg@rpi.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01527-9
PII: S 0002-9947(96)01527-9
Received by editor(s): June 1, 1994
Received by editor(s) in revised form: March 27, 1995
Article copyright: © Copyright 1996 American Mathematical Society