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On the Contribution of Smale to Dynamical Systems

In: From Topology to Computation: Proceedings of the Smalefest

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  • J. Palis

Abstract

It is rare, and, in fact, one may not ever be so lucky in one’s lifetime, to follow rather closely a dramatic change, an absolute upgrading of a branch of Science. In our case, Mathematics, and, more specifically, Dynamical Systems, whose foundations were set by Poincaré about 100 years ago and enriched in the next decades by Birkhoff, Lyapunov, Hadamard, Perron, Morse, Fatou, Julia, and others: One aims at the description of the asymptotic behavior of solutions of differential equations (or trajectories of iterated maps) without necessarily integrating them so as to find explicit expressions for the solutions. Also, in the appropriate setting, one looks for the behavior of solutions of “typical” equations and of “typical” solutions.

Suggested Citation

  • J. Palis, 1993. "On the Contribution of Smale to Dynamical Systems," Springer Books, in: Morris W. Hirsch & Jerrold E. Marsden & Michael Shub (ed.), From Topology to Computation: Proceedings of the Smalefest, chapter 17, pages 165-178, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2740-3_17
    DOI: 10.1007/978-1-4612-2740-3_17
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