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

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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
Dates:	Date Event 15 November 2008 Published
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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