NDLI: Negligibility of small divisor effects in the normal form theory for nearly-integrable Hamiltonians with decaying non-autonomous perturbations

Content Provider	Springer Nature Link
Author	Wiggins, Stephen Fortunati, Alessandro
Copyright Year	2016
Abstract	The paper deals with the problem of the existence of a normal form for a nearly-integrable real-analytic Hamiltonian with aperiodically time-dependent perturbation decaying (slowly) in time. In particular, in the case of an isochronous integrable part, the system can be cast in an exact normal form, regardless of the properties of the frequency vector. The general case is treated by a suitable adaptation of the finite order normalization techniques usually used for Nekhoroshev arguments. The key point is that the so called “geometric part” is not necessary in this case. As a consequence, no hypotheses on the integrable part are required, apart from analyticity. The work, based on two different perturbative approaches developed by Giorgilli et al., is a generalisation of the techniques used by the same authors to treat more specific aperiodically time-dependent problems.
Ending Page	262
Page Count	16
Starting Page	247
File Format	PDF
ISSN	09232958
e-ISSN	15729478
Journal	Celestial Mechanics and Dynamical Astronomy
Issue Number	2
Volume Number	125
Language	English
Publisher	Springer Netherlands
Publisher Date	2016-04-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Nearly integrable Hamiltonian systems, KAM theory Stability Birkhoff normal forms Aperiodic time dependence Astrophysics and Astroparticles Non-autonomous Hamiltonian systems Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion Mechanics Geophysics/Geodesy Dynamical Systems and Ergodic Theory Aerospace Technology and Astronautics Stability problems
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Mathematical Physics Astronomy and Astrophysics Modeling and Simulation Computational Mathematics Space and Planetary Science

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