Drift of slow variables in slow-fast Hamiltonian systems

We study the drift of slow variables in a slow-fast Hamiltonian system with several fast and slow degrees of freedom. Keeping the slow variables frozen, for any periodic trajectory of the fast subsystem we define an action. For a family of periodic orbits, the action is a scalar function of the slow...

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Bibliographic Details
Published in:Physica. D 2008-11, Vol.237 (22), p.2913-2921
Main Authors: Brännström, N., Gelfreich, V.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Heteroclinic
Normal hyperbolicity
Physics
Slow-fast systems
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Summary:We study the drift of slow variables in a slow-fast Hamiltonian system with several fast and slow degrees of freedom. Keeping the slow variables frozen, for any periodic trajectory of the fast subsystem we define an action. For a family of periodic orbits, the action is a scalar function of the slow variables and can be considered as a Hamiltonian function which generates some slow dynamics. These dynamics depend on the family of periodic orbits. Assuming that for the frozen slow variables the fast system has a pair of hyperbolic periodic orbits connected by two transversal heteroclinic trajectories, we prove that for any path composed of a finite sequence of slow trajectories generated by action Hamiltonians, there is a trajectory of the full system whose slow component shadows the path.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2008.05.001