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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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.
|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.|
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|Deposited By:||Ruth Sustaita|
|Deposited On:||13 Aug 2010 17:14|
|Last Modified:||26 Dec 2012 12:18|
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