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- Publications
- Influence
Differential Equations, Dynamical Systems, and Linear Algebra
This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the… Expand
Finding the Homology of Submanifolds with High Confidence from Random Samples
- P. Niyogi, S. Smale, S. Weinberger
- Mathematics, Computer Science
- Discret. Comput. Geom.
- 4 March 2008
TLDR
Differential Equations, Dynamical Systems, and an Introduction to Chaos
- M. Hirsch, S. Smale, R. Devaney
- Mathematics
- 2003
Hirsch, Devaney, and Smale's classic "Differential Equations, Dynamical Systems, and an Introduction to Chaos" has been used by professors as the primary text for undergraduate and graduate level… Expand
Generalized Poincare's Conjecture in Dimensions Greater Than Four
- S. Smale
- Mathematics
- 1 September 1961
Poincare has posed the problem as to whether every simply connected closed 3-manifold (triangulated) is homeomorphic to the 3-sphere, see [18] for example. This problem, still open, is usually called… Expand
Best Choices for Regularization Parameters in Learning Theory: On the Bias—Variance Problem
TLDR
DIFFEOMORPHISMS OF THE 2-SPHERE
- S. Smale
- Mathematics
- 1 April 1959
The analogue of Theorem A for the topological case was proved by H. Kneser [2]. The problem in his case seems to be of a different nature from the differentiable case. J. Munkres [3] has proved that… Expand
A generalized Morse theory
1. Abstract theory. Let M be a C-Riemannian manifold without boundary modeled on a separable Hubert space (see Lang [3]). For pÇzM we denote by ( , )p the inner product in the tangent space Mp and we… Expand
On Gradient Dynamical Systems
- S. Smale
- Mathematics
- 1 July 1961
We consider in this paper a Co vector field X on a Co compact manifold Mn (&M, the boundary of M, may be empty or not) satisfying the following conditions: (1) At each singular point /8 of X, there… Expand
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