The Collected Papers of Stephen Smale

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 own retrospective views.

Foreword
Foreword (77 KB)

Sample Chapter(s)
Research Themes (380 KB)
Smale and Nonlinear Analysis: A Personal Perspective (615 KB)
On the Work of Steve Smale on the Theory of Computation (1 MB)

• Volume I:
  • Research Themes
  • Luncheon Talk and Nomination for Stephen Smale (R Bott)
  • Some Recollections of the Early Work of Steve Smale (M M Peixoto)
  • Luncheon Talk (R Thorn)
  • Banquet Address at the Smalefest (E C Zeeman)
  • Some Retrospective Remarks
  • Part I. Topology:
    • The Work of Stephen Smale in Differential Topology (M Hirsch)
    • A Note on Open Maps
    • A Vietoris Mapping Theorem for Homotopy
    • Regular Curves on Riemannian Manifolds
    • On the Immersion of Manifolds in Euclidean Space (with R K Lashof)
    • Self-Intersections of Immersed Manifolds (with R K Lashof)
    • A Classification of Immersions of the Two-Sphere
    • The Classification of Immersions of Spheres in Euclidean Spaces
    • Diffeomorphisms of the 2-Sphere
    • On Involutions of the 3-Sphere (with M Hirsch)
    • The Generalized Poincare Conjecture in Higher Dimensions
    • On Gradient Dynamical Systems
    • Generalized Poincaré Conjecture in Dimensions Greater Than Four
    • Differentiable and Combinatorial Structures on Manifolds
    • On the Structure of 5-Manifolds
    • A Survey of Some Recent Developments in Differential Topology
    • The Story of the Higher Dimensional Poincaré Conjecture (What actually happened on the beaches of Rio)
  • Part II. Economics:
    • Stephen Smale and the Economic Theory of General Equilibrium (G Debreu)
    • Global Analysis and Economics, I: Pareto Optimum and a Generalization of Morse Theory
    • Global Analysis and Economics, IIA: Extension of a Theorem of Debreu
    • Global Analysis and Economics, III: Pareto Optima and Price Equilibria
    • Global Analysis and Economics IV: Finiteness and Stability of Equilibria with General Consumption Sets and Production
    • Global Analysis and Economics V: Pareto Theory with Constraints
    • Dynamics in General Equilibrium Theory
    • Global Analysis and Economics VI: Geometric Analysis of Pareto Optima and Price Equilibria under Classical Hypotheses
    • A Convergent Process of Price Adjustment and Global Newton Methods
    • Exchange Processes with Price Adjustment
    • Some Dynamical Questions in Mathematical Economics
    • An Approach to the Analysis of Dynamic Processes in Economic Systems
    • On Comparative Statics and Bifurcation in Economic Equilibrium Theory
    • The Prisoner's Dilemma and Dynamical Systems Associated to Non-cooperative Games
    • Global Analysis and Economics
    • Gerard Debreu Wins the Nobel Prize
    • Global Analysis in Economic Theory
  • Part III. Miscellaneous:
    • Scientists and the Arms Race
    • On the Steps of Moscow University
    • Some Autobiographical Notes
    • Mathematical Problems for the Next Century
• Volume II:
  • Part IV. Calculus of Variations (Global Analysis) and PDE's:
    • Smale and Nonlinear Analysis: A Personal Perspective
    • A Generalized Morse Theory
    • Morse Theory and a Non-Linear Generalization of the Dirichlet Problem
    • On the Calculus of Variations
    • An Infinite Dimensional Version of Sard's Theorem
    • On the Morse Index Theorem
    • Corrigendum: On the Morse Index Theorem
    • What is Global Analysis?
    • Book Review on "Global Variational Analysis: Weierstrass Integrals on a Riemannian Manifold" by Marston Morse
    • Smooth Solutions of the Heat and Wave Equations
  • Part V. Dynamics:
    • On the Contribution of Smale to Dynamical Systems (J Palis)
    • Discussion (S Newhouse, R F Williams and others)
    • Morse Inequalities for a Dynamical System
    • On Dynamical Systems
    • Dynamical Systems and the Topological Conjugacy Problem for Diffeomorphisms
    • Stable Manifolds for Differential Equations and Diffeomorphisms
    • A Structurally Stable Differentiable Homeomorphism with an Infinite Number of Periodic Points
    • Diffeomorphisms with Many Periodic Points
    • Structurally Stable Systems are Not Dense
    • Dynamical Systems on n-Dimensional Manifolds
    • Differentiable Dynamical Systems
    • Nongenericity of Ω-stability (with R Abraham)
    • Structural Stability Theorems (with J Palis)
    • Notes on Differentiable Dynamical Systems
    • The Ω-stability Theorem
    • Stability and Genericity in Dynamical Systems
    • Beyond Hyperbolicity (with M Shub)
    • Stability and Isotopy in Discrete Dynamical Systems
    • Dynamical Systems on Manifolds
    • Dynamical Systems and Turbulence
    • Review of "Catastrophe Theory: Selected Papers, 1972–1977" by E C Zeeman
    • On The Problem of Reviving the Ergodic Hypothesis of Boltzmann and Birkhoff
    • On How I Got Started in Dynamical Systems
    • Dynamics Retrospective: Great Problems, Attempts that Failed
    • What is Chaos?
    • Finding a Horseshoe on the Beaches of Rio
    • The Work of Curtis T McMullen
  • Part VI. Mechanics:
    • Steve Smale and Geometric Mechanics (J E Marsden)
    • Topology and Mechanics. I
    • Topology and Mechanics. II: The Planar n-Body Problem
    • Problems on the Nature of Relative Equilibria in Celestial Mechanics
    • Personal Perspectives on Mathematics and Mechanics
  • Part VII. Biology, Electric Circuits, Mathematical Programming:
    • On the Mathematical Foundations of Electrical Circuit Theory
    • A Mathematical Model of Two Cells via Turing's Equation
    • Optimizing Several Functions
    • Sufficient Conditions for an Optimum
    • The Qualitative Analysis of a Difference Equation of Population Growth (with R F Williams)
    • On the Differential Equations of Species in Competition
    • The Problem of the Average Speed of the Simplex Method
    • On the Average Number of Steps of the Simplex Method of Linear ProgramminG
• Volume III:
  • Part VIII. Theory of Computation:
    • On the Work of Steve Smale on the Theory of Computation (M Shub)
    • The Work of Steve Smale on the Theory of Computation: 1990–1999 (L Blum and F Cucker)
    • On Algorithms for Solving f(x) = 0 (with M Hirsch)
    • The Fundamental Theorem of Algebra and Complexity Theory
    • Computational Complexity: On the Geometry of Polynomials and a Theory of Cost: Part I (with M Hirsch)
    • On The Efficiency of Algorithms of Analysis
    • Computational Complexity: On the Geometry of Polynomials and a Theory of Cost: II (with M Hirsch)
    • On the Existence of Generally Convergent Algorithms (with M Hirsch)
    • Newton's Method Estimates from Data at One Point
    • On the Topology of Algorithms, I
    • Algorithms for Solving Equations
    • The Newtonian Contribution to Our Understanding of the Computer
    • On a Theory of Computation and Complexity Over the Real Numbers: NP-completeness, Recursive Functions and Universal Machines (with L Blum and M Shub)
    • Some Remarks on the Foundations of Numerical Analysis
    • Theory of Computation
    • Complexity of Bezout's Theorem. I: Geometric Aspects (with M Hirsch)
    • Complexity of Bezout's Theorem II: Volumes and Probabilities (with M Hirsch)
    • Complexity of Bezout's Theorem: III. Condition Number and Packing (with M Hirsch)
    • Complexity of Bezout's Theorem IV: Probability of Success; Extensions (with M Hirsch)
    • Complexity of Bezout's Theorem V: Polynomial Time (with M Hirsch)
    • The Gödel Incompleteness Theorem and Decidability over a Ring (with L Blum)
    • Separation of Complexity Classes in Koiran's Weak Model (with F Cucker and M Shub)
    • On the Intractability of Hilbert's Nullstellensatz and an Algebraic Version of "NP ≠ P?" (with M Hirsch)
    • Complexity and Real Computation: A Manifesto (with L Blum, F Cucker and M Shub)
    • Algebraic Settings for the Problem "P ≠ NP?" (with L Blum, F Cucker and M Shub)
    • Complexity Theory and Numerical Analysis
    • Some Lower Bounds for the Complexity of Continuation Methods (with J-P Dedieu)
    • A Polynomial Time Algorithm for Diophantine Equations in One Variable (with F Cucker and P Koiran)
    • Complexity Estimates Depending on Condition and Round-off Error (with F Cucker)