Marsden, Jerrold E. (1993) Steve Smale and Geometric Mechanics. In: From Topology to Computation: Proceedings of the Smalefest. Springer-Verlag , New York, pp. 499-516. ISBN 9780387979328 http://resolver.caltech.edu/CaltechAUTHORS:20100830-110933848
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Thus, one can say-perhaps with only a slight danger of oversimplification- that reduction theory synthesises the work of Smale, Arnold (and their predecesors of course) into a bundle, with Smale as the base and Arnold as the fiber. This bundle has interesting topology and carries mechanical connections (with associated Chern classes and Hannay-Berry phases) and has interesting singularities (Arms, Marsden, and Moncrief, Guillemin and Sternberg, Atiyab, and otbers). We will describe some of these features later.
|Item Type:||Book Section|
|Additional Information:||© 1993 Springer-Verlag New York. Inc. Research partially supported by NSF Grant DMS-8922704 and DOE Contract DE-FG03·88ER2S064. Papers presented at an international research conference in honor of Stephen Smale's 60th birthday, held Aug. 5-9, 1990 in Berkeley.|
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|Deposited By:||Ruth Sustaita|
|Deposited On:||14 Sep 2010 19:03|
|Last Modified:||26 Dec 2012 12:22|
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