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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. 769-794.
ISSN 0010-3616

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1007/s00220-008-0518-1

## 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 |
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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 |

Official 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) |

References: | 1. Afraimovich, V.S., Shilnikov, L.P.: On critical sets of Morse-Smale systems. Trans. Moscow Math. |

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

Data sourced from Thomson Reuters' Web of Knowledge

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