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arXiv · 0710.1576

Drift of slow variables in slow-fast Hamiltonian systems

N. Brännström·V. Gelfreich
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Abstract

We study the drift of slow variables in a slow-fast Hamiltonian system with several fast and slow degrees of freedom. For any periodic trajectory of the fast subsystem with the frozen slow variables 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 the fast system with the frozen slow variables 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.

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N. Brännström, V. Gelfreich. 2007-10-15. Drift of slow variables in slow-fast Hamiltonian systems. https://doi.org/10.1016/j.physd.2008.05.001

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