Steve Smale and Geometric Mechanics

Jerrold E. Marsden

Chapter 45 in From Topology to Computation: Proceedings of the Smalefest, 1993, pp 499-516 from Springer

Abstract: Abstract In the period 1960–1965, geometric mechanics was “in the air.” Some key papers were available, such as Arnold’s work on KAM theory and a little had made it into textbooks, such as Mackey’s book on quantum mechanics and Sternberg’s book on differential geometry. In this period, Steve was working on his dynamical systems program. His survey article (Smale [1967]) contained important remarks on how geometric mechanics (specifically Hamiltonian systems on symplectic manifolds) fits into the larger dynamical systems framework. In 1966 at Princeton, Abraham ran a seminar using a preprint of the survey article and it was through this paper that I first encountered Smale’s work. After he visited the seminar, the importance of what he was doing was obvious; also, it became evident that there was great power in asking simple, penetrating, and sometimes even seemingly naive questions. I should add that in the mathematical physics seminar at Princeton that I also had the good fortune of attending, Eugene Wigner had a remarkably similar aura.

Keywords: Relative Equilibrium; Symplectic Manifold; Discrete Symmetry; Geometric Phasis; Reduction Theory (search for similar items in EconPapers)
Date: 1993
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DOI: 10.1007/978-1-4612-2740-3_45

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