The Collected Papers of Stephen Smale

by Smale, Stephen; Wong, R.

• ISBN13: 9789810243074
• ISBN10: 9810243073
• Format: Hardcover
• Copyright: 2000-08-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

Stephen smale is one of the great mathematicians of the 20th century. His work encompasses a wide variety of subjects: differential topology, dynamical systems, calculus of variations, theory of computation, mechanics and mathematical economy. In all these subjects he has left the imprint of collection of fundamental results. He has obtain several distinctions, including the Fields Medal, he Veblen Prize, the Chauvenet Prize, the von Neumann Award and the National Medal of Science.This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his one retrospective views.

Table of Contents

Research Themes	1	(7)
Luncheon Talk and Nomination for Stephen Smale	8	(6)
R. Bott
Some Recollections of the Early Work of Steve Smale	14	(3)
M.M. Peixoto
Luncheon Talk	17	(3)
R. Thom
Banquet Address at the Smalefest	20	(2)
E.C. Zeeman
Some Retrospective Remarks	22	(7)
Part I. Topology
The Work of Stephen Smale in Differential Topology	29	(24)
M. Hirsch
A Note on Open Maps	53	(3)
A Vietoris Mapping Theorem for Homotopy	56	(7)
Regular Curves on Riemannian Manifolds	63	(21)
On the Immersion of Manifolds in Euclidean Space	84	(22)
R. K. Lashof
Self-Intersections of Immersed Manifolds	106	(15)
R. K. Lashof
A Classification of Immersions of the Two-Sphere	121	(10)
The Classification of Immersions of Spheres in Euclidean Spaces	131	(18)
Diffeomorphisms of the 2-Sphere	149	(6)
On Involutions of the 3-Sphere	155	(8)
M. Hirsch
The Generalized Poincare Conjecture in Higher Dimensions	163	(3)
On Gradient Dynamical Systems	166	(8)
Generalized Poincare's Conjecture in Dimensions Greater Than Four	174	(16)
Differentiable and Combinatorial Structures on Manifolds	190	(5)
On the Structure of 5-Manifolds	195	(9)
On the Structure of Manifolds	204	(13)
A Survey of Some Recent Developments in Differential Topology	217	(15)
The Story of the Higher Dimensional Poincare Conjecture (What Actually happened on the beaches of Rio)	232	(11)
Part II. Economics
Stephen Smale and the Economic Theory of General Equilibrium	243	(16)
G. Debreu
Global Analysis and Economics, I: Pareto optimum and a generalization of Morse theory	259	(12)
Global Analysis and Economics, IIA: Extension of a theorem of Debreu	271	(14)
Global Analysis and Economics, III: Pareto optima and price equilibria	285	(11)
Global Analysis and Economics, IV: Finiteness and stability of equilibria with general consumption sets and production	296	(9)
Global Analysis and Economics, V: Pareto theory with constraints	305	(9)
Dynamics in general equilibrium theory	314	(7)
Global Analysis and Economics, VI: Geometric Analysis of Pareto Optima and price equilibria under classical hypotheses	321	(14)
A Convergent Process of Price Adjustment and Global Newton Methods	335	(14)
Exchange Processes with Price Adjustment	349	(16)
Some Dynamical Questions in Mathematical Economics	365	(3)
An Approach to the Analysis of Dynamic Processes in Economic Systems	368	(5)
On Comparative Statics and Bifurcation in Economic Equilibrium Theory	373	(7)
The Prisoner's Dilemma and Dynamical Systems Associated to Non-Cooperative Games	380	(18)
Global Analysis and Economics	398	(40)
Gerard Debreu Wins the Nobel Prize	438	(2)
Global Analysis in Economic Theory	440	(5)
Part III. Miscellaneous
Scientists and the Arms Race	445	(9)
On the Steps of Moscow University	454	(7)
Some Autobiographical Notes	461	(19)
Mathematical Problems for the Next Century	480	(11)
Part IV. Calculus of Variations (Global Analysis) and PDE's
Smale and Nonlinear Analysis: A Personal perspective	491	(12)
A. J. Tromba
A Generalized Morse Theory	503	(8)
R. Palais
Morse Theory and a Non-Linear Generalization of the Dirichlet Problem	511	(15)
On the Calculus of Variations	526	(3)
An Infinite Dimensional Version of Sard's Theorem	529	(6)
On the Morse Index Theorem	535	(7)
A correction to ``On the Morse Index Theorem''	542	(2)
What is Global Analysis?	544	(6)
Book Review on ``Global Variational Analysis: Weierstrass Integrals on a Riemannian Manifold''	550	(11)
Marston Morse
Smooth Solutions of the Heat and Wave Equations	561	(14)
Part V. Dynamics
On the Contribution of Samle to Dynamical Systems	575	(14)
J. Palis
Discussions	589	(7)
S. Newhouse
R. F. Williams
Morse Inequalities for a Dynamical System	596	(7)
On Dynamical Systems	603	(4)
Dynamical Systems and the Topological Conjugacy Problem for Diffeomorphisms	607	(7)
Stable Manifolds for Differential Equations and Diffeomorphisms	614	(20)
A Structurally Stable Differentiable Homeomorphism with and Infinite Number of Periodic Points	634	(2)
Diffeomorphisms with Many Periodic Points	636	(18)
Structurally Stable Systems Are Not Dense	654	(6)
Dynamical Systems on n-Dimensional Manifolds	660	(4)
Differentiable Dynamical Systems	664	(71)
Nongenericity of Ω-Stability	735	(4)
R. Abraham
Structural Stability Theorems	739	(9)
J. Palis
Notes on Differential Dynamical Systems	748	(11)
The Ω-Stability Theorem	759	(9)
Stability and Genericity in Dynamical Systems	768	(8)
Beyond Hyperbolicity	776	(5)
M. Shub
Stability and Isotopy in Discrete Dynamical Systems	781	(4)
Differential Equations	785	(6)
Dynamical Systems and Turbulence	791	(23)
Review of ``Catastrophe Theory: Selected Papers, 1972-1977''	814	(9)
E. C. Zeeman
On the Problem of Reviving the Ergodic Hypothesis of Boltzmann and Birkhoff	823	(8)
On How I Got Started in Dynamical Systems	831	(5)
Dynamics Retrospective: Great Problems, attempts that failed	836	(7)
What is Chaos?	843	(16)
Finding a Horseshoe on the Beaches of Rio	859	(6)
The Work of Curtis T. McMullen	865	(6)
Part VI. Mechanics
Steve Smale and Geometric Mechanics	871	(18)
J. E. Marsden
Topology and Mechanics, I.	889	(27)
Topology and Mechanics, II	916	(20)
Problems on the Nature of Relative Equilibria in Celestial Mechanics	936	(5)
Personal Perspectives on Mathematics and Mechanics	941	(10)
Part VII. Biology, Electric Circuits, Mathematical Programming
On the Mathematical Foundations of Electrical Circuit Theory	951	(18)
A Mathematical Model of Two Cells via Turing's Equation	969	(10)
Optimizing Several Functions	979	(7)
Sufficient Conditions for an Optimum	986	(7)
The Qualitative Analysis of a Difference Equation of Population Growth	993	(4)
R. F. Williams
On the Differential Equations of Species in Competition	997	(3)
The Problem of the Average Speed of the Simplex Method	1000	(10)
On the Average Number of Steps of the Simplex Method of Linear Programming	1010	(25)
Part VIII. Theory of Computation
On the Work of Steve Smale on the Theory of Computation	1035	(21)
M. Shub
The Work of Steve Smale on the Theory of Computation: 1990-1999	1056	(20)
L. Blum
F. Cucker
On Algorithms for Solving f(x)=0	1076	(32)
M. Hirsch
The fundamental Theorem of Algebra and Complexity Theory	1108	(36)
Computational Complexity: On the geometry of polynomials and a theory of cost, Part I	1144	(36)
M. Shub
On the Efficiency of Algorithms of Analysis	1180	(35)
Computational Complexity: On the Geometry of polynomials and a theory of cost, Part II	1215	(17)
M. Shub
On the Existence of Generally Convergent Algorithms	1232	(10)
M. Shub
Newton's Method Estimates form Data at One Point	1242	(12)
On the Topology of Algorithms, I.	1254	(9)
Algorithms for Solving Equations	1263	(24)
The Newtonian Contribution to Our Understanding of the Computer	1287	(6)
On a Theory of Computation and Complexity over the Real Numbers: NP-completeness, recursive functions and universal machines	1293	(46)
L. Blum
M. Shub
Some Remarks on the Foundations of Numerical Analysis	1339	(10)
Theory of Computation	1349	(10)
Complexity of Bezout's Theorem I: Geometric aspects	1359	(43)
M. Shub
Complexity of Bezout's Theorem II: Volumes and probabilities	1402	(19)
M. Shub
Complexity of Bezout's Theorem III: Condition number and packing	1421	(11)
M. Shub
Complexity of Bezout's Theorem IV: Probability of success: Extensions	1432	(21)
M. Shub
Complexity of Bezout's Theorem V: Polynomial time	1453	(24)
M. Shub
The Godel Incompleteness Theorem and Decidability over a Ring	1477	(19)
L. Blum
Separation of Complexity Classes in Koiran's Weak Model	1496	(12)
F. Cucker
2M. Shub
On the Intractability of Hilbert's Nullstellenstaz and an Algerbraic Version of ``NP≠P?''	1508	(8)
M. Shub
Complexity and Real Computation: A Manifesto	1516	(24)
L. Blum
F. Cucker
M. Shub
Algebraic Settings for the Problem ``P≠NP?''	1540	(20)
L. Blum
F. Cucker
M. Shub
Complexity Theory and Numerical Analysis	1560	(29)
Some Lower Bounds for the Complexity of Continuation Methods	1589	(12)
J.-P. Dedieu
A Polynomial Time algorithm for Diophantine Equations in One Variable	1601	(9)
F. Cucker
P. Koiran
Complexity Estimates Depending on Condition and Round-off Error	1610
F. Cucker