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Drift of slow variables in slow-fast Hamiltonian systems

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Brännström, Niklas and Gelfreich, Vassili. (2008) Drift of slow variables in slow-fast Hamiltonian systems. Physica D: Nonlinear Phenomena, Vol.237 (No.22). pp. 2913-2921. ISSN 0167-2789

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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. 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. (C) 2008 Elsevier B.V. All rights reserved.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Hamiltonian systems, Differentiable dynamical systems
Journal or Publication Title: Physica D: Nonlinear Phenomena
Publisher: Elsevier BV
ISSN: 0167-2789
Official Date: 15 November 2008
Volume: Vol.237
Number: No.22
Number of Pages: 9
Page Range: pp. 2913-2921
Identification Number: 10.1016/j.physd.2008.05.001
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Foundation Blanceflor Boncompagni-Ludovisi, nee Bildt
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URI: http://wrap.warwick.ac.uk/id/eprint/29059

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