Sergey Bolotin and Robert MacKay 1997 Nonlinearity 10 1015 doi:10.1088/0951-7715/10/5/001
Sergey Bolotin
and Robert MacKay![]()
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.
45.20.Jj Lagrangian and Hamiltonian mechanics
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
70K44 Homoclinic and heteroclinic trajectories
37J30 Obstructions to integrability (nonintegrability criteria)
Issue 5 (September 1997)
Received 16 August 1996, in final form 5 June 1997
Sergey Bolotin and Robert MacKay 1997 Nonlinearity 10 1015
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