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arXiv · 1405.1268

Persistence of Diophantine flows for quadratic nearly-integrable Hamiltonians under slowly decaying aperiodic time dependence

Alessandro Fortunati·Stephen Wiggins
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Abstract

The aim of this paper is to prove a Kolmogorov-type result for a nearly-integrable Hamiltonian, quadratic in the actions, with an aperiodic time dependence. The existence of a torus with a prefixed Diophantine frequency is shown in the forced system, provided that the perturbation is real-analytic and (exponentially) decaying with time. The advantage consists of the possibility to choose an arbitrarily small decaying coefficient, consistently with the perturbation size.

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Alessandro Fortunati, Stephen Wiggins. 2014-05-06. Persistence of Diophantine flows for quadratic nearly-integrable Hamiltonians under slowly decaying aperiodic time dependence. https://doi.org/10.1134/s1560354714050062

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