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A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam

Holmes, Philip and Marsden, Jerrold E. (1981) A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam. Archive for Rational Mechanics and Analysis, 76 (1). pp. 135-165. ISSN 0003-9527. http://resolver.caltech.edu/CaltechAUTHORS:20100811-095206370

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Abstract

This paper delineates a class of time-periodically perturved evolution equations in a Banach space whose associated Poincar´e map contains a Smale horseshoe. This implies that such systems possess periodic orbits with arbitrarily high period. The method uses techniques originally due to Melnikov and applies to systems of the form x˙ = f0(x) + "f1(x, t), where x˙ = f0(x) is Hamiltonian and has a homoclinic orbit. We give an example from structural mechanics: sinusoidally forced vibrations of a buckled beam.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/BF00251249DOIUNSPECIFIED
http://www.springerlink.com/content/u288jv71p7127880/PublisherUNSPECIFIED
Additional Information:© 1981 Springer. 1981. This version: July 20, 1994. Communicated by D. D. Joseph. Research partially supported by NSF Contract DMS 89-19074 and CTS 89-06343. We thank Mary Silber and Vivien Kirk for helpful discussions on the Hamiltonian structure of normal forms. Research partially supported by DOE Contract DE-FGO3-92ER25129.
Funders:
Funding AgencyGrant Number
NSFDMS 89-19074
NSFCTS 89-06343
Department of EnergyDE-FGO3-92ER25129
Record Number:CaltechAUTHORS:20100811-095206370
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100811-095206370
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19392
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:13 Aug 2010 17:14
Last Modified:26 Dec 2012 12:18

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