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Chaos in dynamical systems by the Poincaré-Melnikov-Arnold method

Marsden, Jerrold E. (1984) Chaos in dynamical systems by the Poincaré-Melnikov-Arnold method. In: Chaos in Nonlinear Dynamical Systems. Society for Industrial and Applied Mathematics , Philadelphia, pp. 19-31. ISBN 9780898710526 http://resolver.caltech.edu/CaltechAUTHORS:20100830-082935945

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Abstract

Methods proving the existence of chaos in the sense of Poincaré-Birkhoff-Smale horseshoes are presented. We shall concentrate on explicitly verifiable results that apply to specific examples such as the ordinary differential equations for a forced pendulum, and for superfluid He and the partial differential equation describing the oscillations off a beam. Some discussion of the difficulties the method encounters near an elliptic fixed point is given.


Item Type:Book Section
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http://www.cds.caltech.edu/~marsden/bib/1984/16-Ma1984/AuthorUNSPECIFIED
Additional Information:© 1984, SIAM. This report was prepared as an account of work sponsored by the Center of Pure and Applied Mathematics. Neither the Center nor the Department of Mathematics, makes any warranty expressed or implied, or assumes any legal liability or responsability for the accuracy, completeness or usefulness of any information or process disclosed.
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Department of EnergyDE-ATO3-02ER12097
Record Number:CaltechAUTHORS:20100830-082935945
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100830-082935945
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ID Code:19694
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:14 Sep 2010 18:42
Last Modified:26 Dec 2012 12:22

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