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From Topology to Computation: Proceedings of the Smalefest Book

From Topology to Computation: Proceedings of the Smalefest
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From Topology to Computation: Proceedings of the Smalefest, This volume is a Festschrift for Stephen Smale's 60th birthday; most of the chapters are based on papers given at a symposium in his honor at the University of California at Berkeley. The contributions reflect the breadth of Smale's interests, ranging ove, From Topology to Computation: Proceedings of the Smalefest
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  • From Topology to Computation: Proceedings of the Smalefest
  • Written by author Morris W. Hirsch
  • Published by Springer-Verlag New York, LLC, 7/31/2012
  • This volume is a Festschrift for Stephen Smale's 60th birthday; most of the chapters are based on papers given at a symposium in his honor at the University of California at Berkeley. The contributions reflect the breadth of Smale's interests, ranging ove
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Book Categories

Authors

Preface
Contributors
Research Themes
Conference Schedule, Smalefest, August 5-9, 1990
1 Some Autobiographical Notes 3
2 On How I Got Started in Dynamical Systems, 1959-1962 22
3 The Story of the Higher Dimensional Poincare Conjecture (What Actually Happened on the Beaches of Rio) 27
4 On the Steps of Moscow University 41
5 Professional Biography, Bibliography, and Graduate Students 53
6 Luncheon Talk and Nomination for Stephen Smale 67
7 Some Recollections of the Early Work of Steve Smale 73
8 Luncheon Talk 76
9 Banquet Address at the Smalefest 79
10 The Work of Stephen Smale in Differential Topology 83
11 Discussion 107
12 Note on the History of Immersion Theory 114
13 The Smale-Hirsch Principle in Catastrophe Theory 117
14 Stephen Smale and the Economic Theory of General Equilibrium 131
15 Topology and Economics: The Contribution of Stephen Smale 147
16 Comments 162
17 On the Contribution of Smale to Dynamical Systems 165
18 Discussion 179
19 Recurrent Sets for Planar Homeomorphisms 186
20 Convergence of Finite-Element Solutions for Nonlinear PDEs 196
21 Ergodic Theory of Chaotic Dynamical Systems 201
22 Beyond Hyperbolicity: Expansion Properties of One-Dimensional Mappings 227
23 Induced Hyperbolicity, Invariant Measures, and Rigidity 237
24 On the Enumerative Geometry of Geodesics 243
25 A Relation Between Newton's Method and Successive Approximations for Quadratic Irrationals 254
26 On Dynamical Systems and the Minimal Surface Equation 259
27 A New Zeta Function, Natural for Links 270
28 On the Work of Steve Smale on the Theory of Computation 281
29 Smale's Work on the Dynamics of Numerical Analysis 302
30 Steve Smale and the Geometry of Ill-Conditioning 305
31 On Smale's Work in the Theory of Computation: From Polynomial Zeros to Continuous Complexity 317
32 The Godel Incompleteness Theorem and Decidability over a Ring 321
33 Ill-Posed Problem Instances 340
34 Cohomology of Braid Groups and Complexity 359
35 The Dynamics of Eigenvalue Computation 368
36 On the Role of Computable Error Estimates in the Analysis of Numerical Approximation Algorithms 387
37 Applications of Topology to Lower Bound Estimates in Computer Science 395
38 On the Distribution of Roots of Random Polynomials 419
39 A General NP-Completeness Theorem 432
40 Some Remarks on Bezout's Theorem and Complexity Theory 443
41 Some Results Relevant to Smale's Reports 456
42 Error Estimates of Ritz-Gelerkin Methods for Indefinite Elliptic Equations 466
43 Smale and Nonlinear Analysis: A Personal Perspective 481
44 Discussion 493
45 Steve Smale and Geometric Mechanics 499
46 Smale's Topological Program in Mechanics and Convexity 517
47 Discussion 530
48 On Paradigm and Method 534
49 Dynamical Systems and the Geometry of Singularly Perturbed Differential Equations 545
50 Cellular Dynamata 557
51 Rough Classification of Integrable Hamiltonians on Four-Dimensional Symplectic Manifolds 561
52 Final Panel 589


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From Topology to Computation: Proceedings of the Smalefest, This volume is a Festschrift for Stephen Smale's 60th birthday; most of the chapters are based on papers given at a symposium in his honor at the University of California at Berkeley. The contributions reflect the breadth of Smale's interests, ranging ove, From Topology to Computation: Proceedings of the Smalefest

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From Topology to Computation: Proceedings of the Smalefest, This volume is a Festschrift for Stephen Smale's 60th birthday; most of the chapters are based on papers given at a symposium in his honor at the University of California at Berkeley. The contributions reflect the breadth of Smale's interests, ranging ove, From Topology to Computation: Proceedings of the Smalefest

From Topology to Computation: Proceedings of the Smalefest

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From Topology to Computation: Proceedings of the Smalefest, This volume is a Festschrift for Stephen Smale's 60th birthday; most of the chapters are based on papers given at a symposium in his honor at the University of California at Berkeley. The contributions reflect the breadth of Smale's interests, ranging ove, From Topology to Computation: Proceedings of the Smalefest

From Topology to Computation: Proceedings of the Smalefest

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