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Regular and Chaotic Dynamics, 2014, Volume 19, Issue 4, Pages 513–522
DOI: https://doi.org/10.1134/S1560354714040078 (Mi rcd178) 		 
Energy Growth for a Nonlinear Oscillator Coupled to a Monochromatic Wave

Dmitry V. Turaevab, Christopher Warnerba, Sergey Zelikab

a University of Surrey, Guildford, Surrey GU2 7XH, UK
b Imperial College, SW7 2 AZ London, UK
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DOI: https://doi.org/10.1134/S1560354714040078
Abstract: A system consisting of a chaotic (billiard-like) oscillator coupled to a linear wave equation in the three-dimensional space is considered. It is shown that the chaotic behavior of the oscillator can cause the transfer of energy from a monochromatic wave to the oscillator, whose energy can grow without bound.
Keywords: delayed equation, invariant manifold, normal hyperbolicity, billiard.
Funding agency Grant number
Leverhulme Trust RPG-279
Ministry of Education and Science of the Russian Federation 14.B37.21.0862
This work was supported by the Leverhulme Trust grant RPG-279 and the Russian Ministry of Education and Science grants 14.B37.21.0862.
Received: 04.04.2014
Accepted: 17.05.2014
Bibliographic databases:
Document Type: Article
MSC: 35B05, 35B42, 37K49
Language: English
Citation: Dmitry V. Turaev, Christopher Warner, Sergey Zelik, “Energy Growth for a Nonlinear Oscillator Coupled to a Monochromatic Wave”, Regul. Chaotic Dyn., 19:4 (2014), 513–522
Citation in format AMSBIB
\Bibitem{TurWarZel14}
\by Dmitry~V.~Turaev, Christopher~Warner, Sergey Zelik
\paper Energy Growth for a Nonlinear Oscillator Coupled to a Monochromatic Wave
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 4
\pages 513--522
\mathnet{http://mi.mathnet.ru/rcd178}
\crossref{https://doi.org/10.1134/S1560354714040078}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3240984}
\zmath{https://zbmath.org/?q=an:1312.35009}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000340380900007}
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