A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
 Philip Holmes,
 Jerrold Marsden
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Abstract
This paper delineates a class of timeperiodically perturbed evolution equations in a Banach space whose associated Poincaré 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=f _{o}(X)+εf _{1}(X,t), where f _{o}(X) is Hamiltonian and has a homoclinic orbit. We give an example from structural mechanics: sinusoidally forced vibrations of a buckled beam.
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 Title
 A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
 Journal

Archive for Rational Mechanics and Analysis
Volume 76, Issue 2 , pp 135165
 Cover Date
 19810601
 DOI
 10.1007/BF00251249
 Print ISSN
 00039527
 Online ISSN
 14320673
 Publisher
 SpringerVerlag
 Additional Links
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 Industry Sectors
 Authors

 Philip Holmes ^{(1)}
 Jerrold Marsden ^{(2)}
 Author Affiliations

 1. Theoretical and Applied Mechanics, Cornell University, Ithaca, New York
 2. Department of Mathematics, University of California, Berkeley