On the Contribution of Smale to Dynamical Systems

J. Palis

Chapter 17 in From Topology to Computation: Proceedings of the Smalefest, 1993, pp 165-178 from Springer

Abstract: 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.

Keywords: Periodic Orbit; Unstable Manifold; Homoclinic Orbit; Ambient Manifold; Morse Inequality (search for similar items in EconPapers)
Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2740-3_17

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DOI: 10.1007/978-1-4612-2740-3_17

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