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Chaotic transport in the homoclinic and heteroclinic tangle regions of quasiperiodically forced two-dimensional dynamical systems

Beigie, Darren and Leonard, Anthony and Wiggins, Stephen (1991) Chaotic transport in the homoclinic and heteroclinic tangle regions of quasiperiodically forced two-dimensional dynamical systems. Nonlinearity, 4 (3). pp. 775-819. ISSN 0951-7715. http://resolver.caltech.edu/CaltechAUTHORS:BEInonlin91

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Abstract

The authors generalize notions of transport in phase space associated with the classical Poincare map reduction of a periodically forced two-dimensional system to apply to a sequence of nonautonomous maps derived from a quasiperiodically forced two-dimensional system. They obtain a global picture of the dynamics in homoclinic and heteroclinic tangles using a sequence of time-dependent two-dimensional lobe structures derived from the invariant global stable and unstable manifolds of one or more normally hyperbolic invariant sets in a Poincare section of an associated autonomous system phase space. The invariant manifold geometry is studied via a generalized Melnikov function. Transport in phase space is specified in terms of two-dimensional lobes mapping from one to another within the sequence of lobe structures, which provides the framework for studying several features of the dynamics associated with chaotic tangles.


Item Type:Article
Additional Information:© 1991 Institute of Physics and IOP Publishing Limited. Received 25 September 1989, in final form 27 November 1990 This material is based upon work supported by a National Science Foundation Graduate Fellowship, the National Science Foundation Presidential Young Investigator Program, the Office of Naval Research Young Investigator Program, and Caltech’s Program in Advanced Technologies, sponsored by Aerojet General, General Motors, and TRW. We thank Peggy Firth and Cecilia Lin for the artwork.
Record Number:CaltechAUTHORS:BEInonlin91
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BEInonlin91
Alternative URL:http://dx.doi.org/10.1088/0951-7715/4/3/008
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4523
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:25 Aug 2006
Last Modified:26 Dec 2012 08:59

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