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