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Horseshoes for autonomous Hamiltonian systems using the Melnikov integral

Published online by Cambridge University Press:  10 December 2009

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Abstract

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This paper applies the Melnikov method to autonomous perturbations of completely integrable Hamiltonian systems. The forcing of the perturbed system is caused by internal oscillations which are not necessarily decoupled. A unified treatment is presented which relates some results of Holmes and Marsden with a result of Lerman and Umanskii. It is also shown that two forms of the Melnikov function by integrals are in fact equal.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Volume 8: Charles Conley Memorial Issue , December 1988 , pp. 395 - 409
Copyright
Copyright © Cambridge University Press 1988

References

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