Unbounded Energy Growth in Hamiltonian Systems with a Slowly Varying Parameter |
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Authors: | Vassili Gelfreich Dmitry Turaev |
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Institution: | (1) Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom;(2) Department of Mathematics, Ben Gurion University of the Negev, Be’er Sheva, 84105, Israel |
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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. |
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Keywords: | |
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