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Unbounded energy growth in Hamiltonian systems with a slowly varying parameter
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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. 769794. ISSN 00103616
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Official URL: http://dx.doi.org/10.1007/s0022000805181
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 nonautonomous perturbations of geodesic flows and Hamiltonian systems with billiardlike 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 nonHamiltonian 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:  00103616  
Official Date:  November 2008  
Dates: 


Volume:  Volume 283  
Number:  Number 3  
Number of Pages:  26  
Page Range:  pp. 769794  
Identifier:  10.1007/s0022000805181  
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), 060172023 (RFFI/MNTI)  
References:  1. Afraimovich, V.S., Shilnikov, L.P.: On critical sets of MorseSmale systems. Trans. Moscow Math. 

URI:  http://wrap.warwick.ac.uk/id/eprint/29488 
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