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A Melnikov Method for Homoclinic Orbits with Many Pulses |
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| Authors: | Roberto Camassa Gregor Kovačič Siu-Kei Tin |
| Affiliation: | (1) Mathematics Department, University of North Carolina, Chapel Hill, North Carolina 27599-3250, USA, US;(2) Mathematical Sciences Department, Rensselaer Polytechnic Institute, Troy, New York 12180-3590, USA, US;(3) Mathematics Department, University of Michigan, Ann Arbor, Michigan 48109, USA, US |
| Abstract: | We present an extension of the Melnikov method which can be used for ascertaining the existence of homoclinic and heteroclinic orbits with many pulses in a class of near‐integrable systems. The Melnikov function in this situation is the sum of the usual Melnikov functions evaluated with some appropriate phase delays. We show that a nonfolding condition which involves the logarithmic derivative of the Melnikov function must be satisfied in addition to the usual transversality conditions in order for homoclinic orbits with more than one pulse to exist. (Accepted December 2, 1996) |
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