From Topology to Computation

1: Autobiographical Material.- 1 Some Autobiographical Notes.- 2 On How I Got Started in Dynamical Systems, 1959–1962.- 3 The Story of the Higher Dimensional Poincaré Conjecture (What Actually Happened on the Beaches of Rio).- 4 On the Steps of Moscow University.- 5 Professional Biography, Bibliography, and Graduate Students.- 2: Informal Talks.- 6 Luncheon Talk and Nomination for Stephen Smale.- 7 Some Recollections of the Early Work of Steve Smale.- 8 Luncheon Talk.- 9 Banquet Address at the Smalefest.- 3: Differential Topology.- 10 The Work of Stephen Smale in Differential Topology.- Discussions.- 11 Discussion.- 12 Note on the History of Immersion Theory.- Contributed Papers.- 13 The Smale—Hirsch Principle in Catastrophe Theory.- 4: Economics.- 14 Stephen Smale and the Economic Theory of General Equilibrium.- Discussions.- 15 Topology and Economics: The Contribution of Stephen Smale.- 16 Comments.- 5: Dynamical Systems.- 17 On the Contribution of Smale to Dynamical Systems.- Discussions.- 18 Discussion.- Contributed Papers.- 19 Recurrent Sets for Planar Homeomorphisms.- 20 Convergence of Finite-Element Solutions for Nonlinear PDEs.- 21 Ergodic Theory of Chaotic Dynamical Systems.- 22 Beyond Hyperbolicity: Expansion Properties of One-Dimensional Mappings.- 23 Induced Hyperbolicity, Invariant Measures, and Rigidity.- 24 On the Enumerative Geometry of Geodesies.- 25 A Relation Between Newton’s Method and Successive Approximations for Quadratic Irrationals.- 26 On Dynamical Systems and the Minimal Surface Equation.- 27 A New Zeta Function, Natural for Links.- 6: Theory of Computation.- 28 On the Work of Steve Smale on the Theory of Computation.- Discussions.- 29 Smale’s Work on the Dynamics of Numerical Analysis.- 30 Steve Smale and the Geometry of Ill-Conditioning.- 31 On Smale’s Work in the Theory of Computation: From Polynomial Zeros to Continuous Complexity.- Contributed Papers.- 32 The Gödel Incompleteness Theorem and Decidability over a Ring.- 33 Ill-Posed Problem Instances.- 34 Cohomology of Braid Groups and Complexity.- 35 The Dynamics of Eigenvalue Computation.- 36 On the Role of Computable Error Estimates in the Analysis of Numerical Approximation Algorithms.- 37 Applications of Topology to Lower Bound Estimates in Computer Science.- 38 On the Distribution of Roots of Random Polynomials.- 39 A General NP-Completeness Theorem.- 40 Some Remarks on Bezout’s Theorem and Complexity Theory.- 41 Some Results Relevant to Smale’s Reports.- 42 Error Estimates of Ritz—Gelerkin Methods for Indefinite Elliptic Equations.- 7: Nonlinear Functional Analysis.- 43 Smale and Nonlinear Analysis: A Personal Perspective.- Discussion.- 44 Discussion.- 8: Applications.- 45 Steve Smale and Geometric Mechanics.- Discussion.- 46 Smale’s Topological Program in Mechanics and Convexity.- 47 Discussion.- Contributed Papers.- 48 On Paradigm and Method.- 49 Dynamical Systems and the Geometry of Singularly Perturbed Differential Equations.- 50 Cellular Dynamata.- 51 Rough Classification of Integrable Hamiltonians on Four-Dimensional Symplectic Manifolds.- 9: Final Panel.- 52 Final Panel.