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A group theoretic approach to the equations of plasma physics

Marsden, Jerrold E. (1982) A group theoretic approach to the equations of plasma physics. Canadian Mathematical Bulletin, 25 (2). pp. 129-142. ISSN 0008-4395. http://resolver.caltech.edu/CaltechAUTHORS:20100825-103110885

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Abstract

This paper concerns the interaction between group theory and classical mechanics in general and with the application of this theory to plasma physics in particular. Mechanics has had a profound role in the historical development of mathematics. Leading original thinkers in pure mathematics such as Newton, Euler, Lagrange, Jacobi, Laplace, Cauchy, Gauss, Riemann, Poincaré, Hilbert, Birkhofï, Smale and Arnold were also great original thinkers in various facets of mechanics. The interaction between mechanics and pure mathematics remains one of the most active and flourishing areas of current research. It is this flavor which I hope to convey in this lecture.


Item Type:Article
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http://www.math.ca/cmb/v25/p129PublisherUNSPECIFIED
Additional Information:© 1982, CMS. Received by the editors September 20, 1981. This paper is based on the Jeffrey-Williams lecture given at the meeting of the Canadian Mathematical Society. Dalhousie University. Halifax. Nova Scotia, May 28. 1981 upon the invitation of the Research Committee of the CMS. Research partially supported by NSF grant MCS-78-0671S, ARO contract DAAG-29-79-C-0086. and the Miller Institute for Basic Research. Much of the work that I will describe below was done in collaboration with Alan Weinstein (see Marsden and Weinstein [1981]). A seminal paper of Morrison [1980] originally shown to us by Allan Kaufman was our starting point. Our ideas were developed in a series of lectures given by both of us to Kaufman's plasma physics-dynamics seminar early in 1981 at Berkeley. The participant's enthusiasm and encouragement were very important. I thank the officers of the Canadian Mathematical Society for the opportunity and honor to present these ideas in the Jeffrey-Williams lecture. I wish to dedicate this lecture to my undergraduate teachers from Toronto who had such a positive influence on my career, especially Professors Atkinson, Coxeter, Davis, Duff, Pillow, Rooney, Rund, Scherk, Scherk and Vanstone. It was through them that I first appreciated the fact that pure and applied mathematics have a magnificant intersection within mathematics.
Funders:
Funding AgencyGrant Number
NSFMCS-78-06718
Army Research Office (ARO)DAAG-29-79-C-0086
Miller Institute for Basic ResearchUNSPECIFIED
Subject Keywords:plasma physics ; equations
Classification Code:AMS (1980): 580. 58E. 58F. 70H. 70W
Record Number:CaltechAUTHORS:20100825-103110885
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100825-103110885
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19656
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:14 Sep 2010 16:36
Last Modified:26 Dec 2012 12:21

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