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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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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

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:

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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