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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. doi:10.1016/j.physd.2008.05.001 ISSN 0167-2789.
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Official URL: http://dx.doi.org/10.1016/j.physd.2008.05.001
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 |
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| Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
| Dates: |
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| Volume: | Vol.237 | ||||
| Number: | No.22 | ||||
| Number of Pages: | 9 | ||||
| Page Range: | pp. 2913-2921 | ||||
| DOI: | 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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