- 07-215 V. Gelfreich, D. Turaev
- Unbounded energy growth in Hamiltonian systems with a slowly varying parameter
Sep 20, 07
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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.