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Multibump orbits near the anti-integrable limit for Lagrangian systems

Sergey Bolotin-+ and Robert MacKay++

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Recommended by H Hofer

We consider Lagrangian systems with Lagrangians , depending slowly on time. In the limit (adiabatic limit) the system becomes autonomous with Lagrangian depending on the parameter t. By using variational methods, for small , we construct trajectories that are close to chains of homoclinic orbits of the limit system. This is a generalization of a result of Cherry, who considered the one-dimensional nondegenerate case. Some multidimensional nondegenerate cases were studied by Palmer. The trajectories we construct are similar to the trajectories of symplectic maps in the so-called anti-integrable limit.


PACS

45.20.Jj Lagrangian and Hamiltonian mechanics

45.10.Na Geometrical and tensorial methods

45.10.Db Variational and optimization methods

MSC

70H03 Lagrange's equations

37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods

70K44 Homoclinic and heteroclinic trajectories

37J30 Obstructions to integrability (nonintegrability criteria)

Subjects

Mathematical physics

Computational physics

Dates

Issue 5 (September 1997)

Received 16 August 1996, in final form 5 June 1997



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