Gelfreich, Vassili and Turaev, Dmitry. (2008) Unbounded energy growth in Hamiltonian systems with a slowly varying parameter. Communications in Mathematical Physics, Volume 283 (Number 3). pp. 769-794. ISSN 0010-3616

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Abstract

We study Hamiltonian systems which depend slowly on time. We show that if the corresponding frozen system has a uniformly hyperbolic invariant set with chaotic behaviour, then the full system has orbits with unbounded energy growth (under very mild genericity assumptions). We also provide formulas for the calculation of the rate of the fastest energy growth. We apply our general theory to non-autonomous perturbations of geodesic flows and Hamiltonian systems with billiard-like and homogeneous potentials. In these examples, we show the existence of orbits with the rates of energy growth that range, depending on the type of perturbation, from linear to exponential in time. Our theory also applies to non-Hamiltonian systems with a first integral.

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
Journal or Publication Title:	Communications in Mathematical Physics
Publisher:	Springer
ISSN:	0010-3616
Date:	November 2008
Volume:	Volume 283
Number:	Number 3
Number of Pages:	26
Page Range:	pp. 769-794
Identification Number:	10.1007/s00220-008-0518-1
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Royal Society (Great Britain), University of Warwick, Israel Science Foundation (ISF), Rossiĭskiĭ fond fundamentalʼnykh issledovaniĭ [Russian Foundation for Basic Research] (RFFI), MNTI
Grant number:	926/04 (ISF), 273/07 (ISF), 06-01-72023 (RFFI/MNTI)
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URI:	http://wrap.warwick.ac.uk/id/eprint/29488

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