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

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.

arXiv commentSeveral corrections in the proof with respect to the previous version. Main statement unchanged

References in corpus (2)

• Twistless KAM tori, quasi flat homoclinic intersections, and other cancellations in the perturbation series of certain completely integrable hamiltonian systems. A review
• Normal Form and Nekhoroshev stability for nearly-integrable Hamiltonian systems with unconditionally slow aperiodic time dependence

Cited by in corpus (3)

• Negligibility of small divisor effects in the normal form theory for nearly-integrable Hamiltonians with decaying non-autonomous perturbations
• A Kolmogorov theorem for nearly-integrable Poisson systems with asymptotically decaying time-dependent perturbation
• Normal forms à la Moser for aperiodically time-dependent Hamiltonians in the vicinity of a hyperbolic equilibrium