Homoclinic trajectories of invariant sets of Hamiltonian systems

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 1997Publisher:Springer Science and Business Media LLCJournal:NoDEA : Nonlinear Differential Equations and Applications, volume 4, pages 359-389 (issn: 1021-9722, eissn: 1420-9004,

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Authors: Bolotin, Sergey;

doi: 10.1007/s000300050020

Homoclinic trajectories of invariant sets of Hamiltonian systems

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Abstract

This paper considers positive definite time-periodic Hamiltonian systems. The author reviews the conditions on equilibria (i.e., local maxima of the potential energy) which guarantee the existence of homoclinic trajectories. He then uses variational methods to establish that similar conditions on Mather sets also guarantee the existence of homoclinic orbits.

Related Organizations

Lomonosov Moscow State University
Russian Federation

Keywords

Stability for nonlinear problems in mechanics, Mather sets, periodic Hamiltonian systems, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, homoclinic trajectories

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