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Stable dynamics in forced systems with sufficiently high/low forcing frequency

Bartuccelli, Michele, Gentile, G and Wright, JA (2016) Stable dynamics in forced systems with sufficiently high/low forcing frequency Chaos, 26, 083108.

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Abstract

We consider a class of parametrically forced Hamiltonian systems with one-and-a-half degrees of freedom and study the stability of the dynamics when the frequency of the forcing is relatively high or low. We show that, provided the frequency of the forcing is sufficiently high, KAM theorem may be applied even when the forcing amplitude is far away from the perturbation regime. A similar result is obtained for sufficiently low frequency forcing, but in that case we need the amplitude of the forcing to be not too large; however we are still able to consider amplitudes of the forcing which are outside of the perturbation regime. Our results are illustrated by means of numerical simulations for the system of a forced cubic oscillator. In addition, we find numerically that the dynamics are stable even when the forcing amplitude is very large (beyond the range of validity of the analytical results), provided the frequency of the forcing is taken correspondingly low.

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Bartuccelli, MicheleM.Bartuccelli@surrey.ac.ukUNSPECIFIED
Gentile, GUNSPECIFIEDUNSPECIFIED
Wright, JAUNSPECIFIEDUNSPECIFIED
Date : 10 August 2016
Identification Number : 10.1063/1.4960614
Copyright Disclaimer : Copyright 2016 American Institute of Physics.
Uncontrolled Keywords : math.DS, math.DS, 34C29, 34D20, 34E14, 58F27, 70H05
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 07 Feb 2017 16:27
Last Modified : 10 Aug 2017 02:08
URI: http://epubs.surrey.ac.uk/id/eprint/813478

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