Multi-bump orbits homoclinic to resonance bands

被引:75
作者
Kaper, TJ [1 ]
Kovacic, G [1 ]
机构
[1] RENSSELAER POLYTECH INST,DEPT MATH SCI,TROY,NY 12180
关键词
D O I
10.1090/S0002-9947-96-01527-9
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 Silnikov 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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收藏
页码:3835 / 3887
页数:53
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