From Topology to Computation: Proceedings of the Smalefest

Front Matter....Pages i-xxix
Front Matter....Pages 1-1
Some Autobiographical Notes....Pages 3-21
On How I Got Started In Dynamical Systems, 1959–1962....Pages 22-26
The Story of the Higher Dimensional Poincaré Conjecture (What Actually Happened on the Beaches of Rio)....Pages 27-40
On the Steps of Moscow University....Pages 41-52
Professional Biography, Bibliography, and Graduate Students....Pages 53-63
Front Matter....Pages 65-65
Luncheon Talk and Nomination for Stephen Smale....Pages 67-72
Some Recollections of the Early Work of Steve Smale....Pages 73-75
Luncheon Talk....Pages 76-78
Banquet Address at the Smalefest....Pages 79-80
Front Matter....Pages 81-81
The Work of Stephen Smale in Differential Topology....Pages 83-106
Discussion....Pages 107-113
Note on the History of Immersion Theory....Pages 114-116
The Smale—Hirsch Principle in Catastrophe Theory....Pages 117-128
Front Matter....Pages 129-129
Stephen Smale and the Economic Theory of General Equilibrium....Pages 131-146
Comments....Pages 162-162
Topology and Economics: The Contribution of Stephen Smale....Pages 147-161
Front Matter....Pages 1-1
On the Contribution of Smale to Dynamical Systems....Pages 165-178
Discussion....Pages 179-185
Recurrent Sets for Planar Homeomorphisms....Pages 186-195
Convergence of Finite-Element Solutions for Nonlinear PDEs....Pages 196-200
Front Matter....Pages 1-1
Ergodic Theory of Chaotic Dynamical Systems....Pages 201-226
Beyond Hyperbolicity: Expansion Properties of One-Dimensional Mappings....Pages 227-236
Induced Hyperbolicity, Invariant Measures, and Rigidity....Pages 237-242
On the Enumerative Geometry of Geodesics....Pages 243-253
A Relation Between Newton’s Method and Successive Approximations for Quadratic Irrationals....Pages 254-258
On Dynamical Systems and the Minimal Surface Equation....Pages 259-269
A New Zeta Function, Natural for Links....Pages 270-278
Front Matter....Pages 279-279
On the Work of Steve Smale on the Theory of Computation....Pages 281-301
Smale’s Work on the Dynamics of Numerical Analysis....Pages 302-304
Steve Smale and the Geometry of Ill-Conditioning....Pages 305-316
On Smale’s Work in the Theory of Computation: From Polynomial Zeros to Continuous Complexity....Pages 317-320
The Gödel Incompleteness Theorem and Decidability over a Ring....Pages 321-339
Ill-Posed Problem Instances....Pages 340-358
Cohomology of Braid Groups and Complexity....Pages 359-367
The Dynamics of Eigenvalue Computation....Pages 368-386
On the Role of Computable Error Estimates in the Analysis of Numerical Approximation Algorithms....Pages 387-394
Applications of Topology to Lower Bound Estimates in Computer Science....Pages 395-418
On the Distribution of Roots of Random Polynomials....Pages 419-431
A General NP-Completeness Theorem....Pages 432-442
Some Remarks on Bezout’s Theorem and Complexity Theory....Pages 443-455
Front Matter....Pages 279-279
Some Results Relevant to Smale’s Reports....Pages 456-465
Error Estimates of Ritz—Gelerkin Methods for Indefinite Elliptic Equations....Pages 466-478
Front Matter....Pages 479-479
Smale and Nonlinear Analysis: A Personal Perspective....Pages 481-492
Discussion....Pages 493-496
Front Matter....Pages 497-497
Steve Smale and Geometric Mechanics....Pages 499-516
Smale’s Topological Program in Mechanics and Convexity....Pages 517-529
Discussion....Pages 530-533
On Paradigm and Method....Pages 534-544
Dynamical Systems and the Geometry of Singularly Perturbed Differential Equations....Pages 545-556
Cellular Dynamata....Pages 557-560
Rough Classification of Integrable Hamiltonians on Four-Dimensional Symplectic Manifolds....Pages 561-586
Front Matter....Pages 587-587
Final Panel....Pages 589-605