Abstract:
The aim of this paper is to extend the result of Giorgilli and Zehnder for aperiodic time dependent systems to a case of nearly integrable convex analytic Hamiltonians. The existence of a normal form and then a stability result are shown in the case of a slow aperiodic time dependence that, under some smallness conditions, is independent of the size of the perturbation.
Keywords:
Hamiltonian systems, Nekhoroshev theorem, aperiodic time dependence.
Citation:
Alessandro Fortunati, Stephen Wiggins, “Normal Form and Nekhoroshev Stability for Nearly Integrable
Hamiltonian Systems with Unconditionally Slow Aperiodic
Time Dependence”, Regul. Chaotic Dyn., 19:3 (2014), 363–373
\Bibitem{ForWig14}
\by Alessandro~Fortunati, Stephen~Wiggins
\paper Normal Form and Nekhoroshev Stability for Nearly Integrable
Hamiltonian Systems with Unconditionally Slow Aperiodic
Time Dependence
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 3
\pages 363--373
\mathnet{http://mi.mathnet.ru/rcd160}
\crossref{https://doi.org/10.1134/S1560354714030071}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3215695}
\zmath{https://zbmath.org/?q=an:1309.70026}
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Linking options:
https://www.mathnet.ru/eng/rcd160
https://www.mathnet.ru/eng/rcd/v19/i3/p363
This publication is cited in the following 8 articles:
A. Fortunati, S. Wiggins, “Transient invariant and quasi-invariant structures in an example of an aperiodically time dependent fluid flow”, Int. J. Bifurcation Chaos, 28:5 (2018), 1830015
Alessandro Fortunati, Stephen Wiggins, “Transient Invariant and Quasi-Invariant Structures in an Example of an Aperiodically Time Dependent Fluid Flow”, Int. J. Bifurcation Chaos, 28:05 (2018), 1830015
A. Fortunati, S. Wiggins, “Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium”, J. Math. Phys., 57:9 (2016), 092703
A. Fortunati, S. Wiggins, “Negligibility of small divisor effects in the normal form theory for nearly-integrable Hamiltonians with decaying non-autonomous perturbations”, Celest. Mech. Dyn. Astron., 125:2 (2016), 247–262
F. Cong, J. Hong, H. Li, “Quasi-effective stability for nearly integrable Hamiltonian systems”, Discrete Contin. Dyn. Syst.-Ser. B, 21:1 (2016), 67–80
Alessandro Fortunati, Stephen Wiggins, Essays in Mathematics and its Applications, 2016, 89
Alessandro Fortunati, Stephen Wiggins, “A Kolmogorov Theorem for Nearly Integrable Poisson Systems with Asymptotically Decaying Time-dependent Perturbation”, Regul. Chaotic Dyn., 20:4 (2015), 476–485
Alessandro Fortunati, Stephen Wiggins, “Persistence of Diophantine Flows for Quadratic Nearly Integrable Hamiltonians under Slowly Decaying Aperiodic Time Dependence”, Regul. Chaotic Dyn., 19:5 (2014), 586–600
Citation in format AMSBIB
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