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Differentiable dynamical systems
S Smale
(1967)
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Invariant Manifolds
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Structural stability on two-dimensional manifolds
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Publication date (Print):
1980
Pages
: 246-252
DOI:
10.1016/S0079-8169(08)61583-4
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Dedication
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pp. vi
Copyright page
pp. vii
Preface
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Notation
pp. vii
Preface
pp. vii
Preface
pp. vii
Preface
pp. xi
Preface
pp. xi
Introduction
pp. xi
Forword
pp. xi
Preface
pp. xi
Instructions to the Reader
pp. xi
Preface
pp. xi
Introduction
pp. xiii
Acknowledgments
pp. xiii
Acknodedgments
pp. xiii
Acknowledgments
pp. xiii
Preface
pp. xiii
Notation Index
pp. xiii
Acknowledgments
pp. xix
Notations and Commonly Used Abbreviations
pp. xix
List of Symbols
pp. xv
Notational Conventions
pp. xv
0. Introduction
pp. xv
List of Symbols
pp. xv
Symbols and Notation
pp. xv
Acknowledgments
pp. xv
Introduction
pp. xv
Preface
pp. xv
Preface to the Second Edition
pp. xvii
Acknowledgments
pp. xvii
List of Spaces and Norms
pp. xvii
Preface to the First Edition
pp. xvii
0.1-7 On Notation and Nomenclature
pp. xxiii
Dedication
pp. xxix
Preface
pp. 1
0 Introduction
pp. 1
Chapter I Riemannian Manifolds
pp. 1
Chapter I Cohomology Groups of G in A
pp. 1
REMOVED: Introduction
pp. 1
Elementary Group Theory
pp. 1
Introduction
pp. 1
Chapter 1 An Introduction to the Homotopy Groups of Spheres
pp. 1
Chapter 1 Preliminaries
pp. 1
Introduction
pp. 1
Introduction to Set Theory
pp. 1
1-5 Preliminaries
pp. 1
Introduction
pp. 1
1 Banach Spaces
pp. 1
I Introductory Topics
pp. 1
Chapter 1 Planar Graphs
pp. 1
I Differentiable Structures
pp. 1
Chapter 1 Riemann's Paper
pp. 1
Chapter 0: Language and Inference
pp. 1
Chapter I Elementary Theory in C”
pp. 1
Chapter 1 Axiomatic Set Theory
pp. 1
Chapter 1 Introduction
pp. 3
1. Equicontinuous Families
pp. 3
Chapter 1 Definition of the Subject
pp. 7
REMOVED: A I Algebraic and differential topology
pp. 7
2. Infinite Products
pp. 7
Chapter 2 History of the Project
pp. 8
Chapter 2 General Properties of Entire Functions of Finite Order
pp. 10
I Single Homomorphisms Iterated
pp. 10
3. Convex Functions
pp. 10
Chapter 3 Case Studies
pp. 11
Chapter I Basic Ideas of Hilbert Space Theory
pp. 11
I Elementary Properties of the Integral in One-Dimensional Space
pp. 12
Chapter 1 Some Simple Examples
pp. 12
Chapter 2 Bridges and Circuits
pp. 16
The Crystallographic Groups
pp. 17
Chapter 2 Operator Theory
pp. 20
4. The Gamma Function
pp. 21
Chapter I Topological Spaces
pp. 22
II The Spaces LpΩ
pp. 23
6-12 The Connection Between Local Linear Lie Groups and Lie Algebras
pp. 23
5. Measure and Integration
pp. 25
II Immersions, Imbeddings, Submanifolds
pp. 25
REMOVED: A II Differential manifolds. Differential geometry
pp. 28
Chapter 2 Equivalent Systems
pp. 30
Chapter 3 Dual Graphs
pp. 30
6. Hausdorff Measures and Dimension
pp. 32
2 Banach Algebras
pp. 35
REMOVED: A III Ordinary differential equations
pp. 35
7. Product Measures
pp. 37
Chapter 3 Linear Functionals
pp. 38
8. The Newtonian Potential
pp. 39
Chapter 1: Logic
pp. 39
Chapter 3 The Minimum Modulus
pp. 39
Chapter 2 The Product Formula for ξ
pp. 41
III Normal Bundle, Tubular Neighborhoods
pp. 42
9. Harmonic Functions and the Poisson Integral
pp. 43
REMOVED: A IV Ergodic theory
pp. 43
II Single Finite Substitutions Iterated
pp. 44
III The Spaces Wm,p Ω
pp. 45
Chapter II Mappings of Cohomology Groups
pp. 47
Chapter 2 Setting up the Adams Spectral Sequence
pp. 48
Chapter 4 Euler's Formula and its Consequences
pp. 48
Chapter 3 Riemann's Main Formula
pp. 49
10. Smooth Functions
pp. 49
REMOVED: A V Partial differential equations
pp. 53
11. Taylor's Formula
pp. 55
Chapter 4 The Weak Topology
pp. 55
Chapter 4 Functions with Real Negative Zeros
pp. 56
Chapter II Topology of Differentiable Manifolds
pp. 57
Chapter 3 Integration of Vector Fields
pp. 57
Chapter II Measure Theory and Hilbert Spaces of Functions
pp. 58
12. The Orthogonal Group
pp. 59
IV Transversality
pp. 60
Chapter 4 Other Areas
pp. 61
Group Representation Theory
pp. 62
Chapter 5 Software Requirements
pp. 62
Chapter 5 Large Circuits
pp. 63
13. Second-Order Differential Operators
pp. 63
Chapter 2: Set Theory
pp. 63
3 Geometry of Hilbert Space
pp. 63
13-19 Solvability and Semisimplicity
pp. 65
Chapter 6 Hardware Requirements
pp. 65
IV Interpolation and Extension Theorems
pp. 66
Chapter 5 General Properties of Functions of Exponential Type
pp. 66
14. Convex Sets
pp. 68
Chapter 4 The Prime Number Theorem
pp. 68
Chapter 7 Practical Advice
pp. 69
15. Convex Functions of Several Variables
pp. 69
Chapter 3 The Classical Adams Spectral Sequence
pp. 70
II Integration in One-Dimensional Space: Further Development
pp. 71
Chapter II Weierstrass Preparation Theorem
pp. 73
REMOVED: A VI Noncommutative harmonic analysis
pp. 73
Chapter 8 Language for Mathematical Experiments
pp. 75
Chapter 6 Colorations
pp. 75
V Foliations
pp. 75
Chapter 5 More about Weak Topologies
pp. 77
16. Analytic Functions of Several Variables
pp. 77
Chapter II Separation Properties
pp. 78
Chapter 5 De la Vallée Poussin's Theorem
pp. 78
Chapter 2 Transitive Models Of Set Theory
pp. 78
Chapter 9 Mathematical Objects—Data Structures
pp. 80
Chapter 4 Linear systems
pp. 81
4 Operators on Hilbert Space and C*-Algebras
pp. 81
17. Linear Topological Spaces
pp. 82
Chapter III Curvature and Homology of Riemannian Manifolds
pp. 82
Chapter 6 Functions of Exponential Type, Restricted on a Line. I. Theorems in the Large
pp. 87
Chapter III Some Properties of Cohomology Groups
pp. 87
Chapter 6 Applications to Analysis
pp. 87
REMOVED: A VII Automorphic forms and modular forms
pp. 89
VI Operations on Manifolds
pp. 90
Chapter 7 Color Functions
pp. 91
18. Distributions
pp. 94
19. Differentiation of Distributions
pp. 95
V Imbeddings of Wm,p Ω)
pp. 96
Chapter 6 Numerical Analysis of the Roots by Euler-MacIaurin Summation
pp. 97
20. Topology of Distributions
pp. 97
REMOVED: A VIII Analytic geometry
pp. 99
20-27 Dressings and Classification of Semisimple Complex Lie Algebras
pp. 100
Chapter 10 Functions—APL Statements
pp. 101
21. The Support of a Distribution
pp. 101
Chapter 7 The Theory of Distributions
pp. 102
Chapter 8 Formulations of the Four-Color Problem
pp. 105
22. Distributions in One Dimension
pp. 108
23. Homogeneous Distributions
pp. 109
Chapter 5 Linearization
pp. 113
REMOVED: A IX Algebraic geometry
pp. 113
Chapter 7 Functions of Exponential Type, Restricted on a Line. II. Asymptotic Behavior in a Half Plane
pp. 114
24. The Analytic Continuation of Distributions
pp. 116
Representations of the Symmetric Groups
pp. 117
Chapter 9 Cubic Graphs
pp. 118
25. The Convolution of a Distribution with a Test Function
pp. 119
Chapter 4 BP-Theory and the Adams-Novikov Spectral Sequence
pp. 121
5 Compact Operators, Fredholm Operators, and Index Theory
pp. 121
III Returning to Single Iterated Homomorphisms
pp. 122
Chapter 11 APL Operators
pp. 123
26. The Convolution of Distributions
pp. 125
VII Handle Presentation Theorem
pp. 127
Chapter III Compactness and Uniformization
pp. 127
27. Harmonic and Subharmonic Distributions
pp. 132
Chapter IV Compact Lie Groups
pp. 133
Chapter 8 Functions of Exponential Type: Connections Between Growth and Distribution of Zeros
pp. 134
Chapter 10 Hadwiger's Conjecture
pp. 134
28. Temperate Distributions
pp. 136
Chapter 7 The Riemann-Siegal Formula
pp. 136
Chapter IV The Cup Product
pp. 137
Chapter 3 Forcing And Generic Models
pp. 138
29. Fourier Transforms of Functions in
pp. 140
Chapter 12 APL Programs—Defined Functions
pp. 141
Chapter III Review from Local Algebra
pp. 142
28-38 Topological and Integration Methods
pp. 143
Chapter 6 Stable Manifolds
pp. 143
VIII The h-Cobordism Theorem
pp. 143
VI Compact Imbeddings of Wm,p Ω
pp. 144
30. Fourier Transforms of Temperate Distributions
pp. 145
Appendix A Solutions to Starred Problems in Chapters 1–4
pp. 146
Chapter V Complex Manifolds
pp. 147
REMOVED: A X Theory of numbers
pp. 149
31. The Convolution of Temperate Distributions
pp. 149
6 The Hardy Spaces
pp. 152
Lie Groups and Lie Algebras
pp. 152
Chapter 9 Uniqueness Theorems
pp. 153
Appendix A: The Construction Definitions
pp. 154
32. Fourier Transforms of Homogeneous Distributions
pp. 159
Appendix B Reflexive Banach Spaces
pp. 161
Chapter 7 Stable Systems
pp. 161
References
pp. 161
33. Periodic Distributions in One Variable
pp. 163
Index
pp. 163
Appendix B: The Consistency of The Axiom of Size
pp. 164
Chapter 11 Critical Graphs
pp. 165
34. Periodic Distributions in Several Variables
pp. 167
IX Framed Manifolds
pp. 167
REMOVED: B I Homological algebra
pp. 167
35. Spherical Harmonics
pp. 167
Appendix C: Axiomatic Equivalence
pp. 169
Index of Constants
pp. 170
Chapter 5 The Chromatic Spectral Sequence
pp. 171
Chapter 8 Large-Scale Computations
pp. 172
Chapter III Theory of Linear Operators in Hilbert Spaces
pp. 173
General Index
pp. 173
Chapter 13 Designing the Experiment
pp. 175
36. Singular Integrals
pp. 175
III Applications to Differential Equations and to Probability Theory
pp. 175
Chapter IV Continuity
pp. 177
7 Toeplitz Operators
pp. 177
VII Fractional Order Spaces
pp. 178
Chapter 10 Growth Theorems
pp. 181
37. Functions of Positive Type
pp. 181
Chapter 14 An Experiment in Heuristic Asymptotics
pp. 182
Chapter 9 The Growth of Zeta as t → ∞ and the Location of Its Zeros
pp. 183
REMOVED: B II Lie groups
pp. 188
IV Several Homomorphisms Iterated
pp. 189
38. Groups of Unitary Transformations
pp. 189
Chapter IV Parameters in Power Series Rings
pp. 191
REMOVED: B III Abstract groups
pp. 192
Chapter 12 Planar 5-Chromatic Graphs
pp. 192
39. Autocorrelation Functions
pp. 195
X Surgery
pp. 195
Chapter V Group Extensions
pp. 196
Appendix A Theory of Manifolds
pp. 197
40. Uniform Distribution Modulo 1
pp. 197
Chapter VI Curvature and Homology of Kaehler Manifolds
pp. 199
REMOVED: B IV Commutative harmonic analysis
pp. 201
41. Schoenberg's Theorem
pp. 203
Chapter 10 Fourier Analysis
pp. 206
Chapter 11 Operators and their Extremal Properties
pp. 206
Compact Lie Groups
pp. 207
42. Distributions of Positive Type
pp. 207
39-50 The Algebraic Approach to Linear Representations
pp. 208
References
pp. 209
REMOVED: B V Von Neumann algebras
pp. 210
43. Paley-Wiener Theorems
pp. 213
Index
pp. 215
REMOVED: B VI Mathematical logic
pp. 215
44. Functions of the Pick Class
pp. 216
Chapter 4 Some Applications Of Forcing
pp. 219
Chapter 6 Morava Stabilizer Algebras
pp. 222
The Rotation Group and Its Representations
pp. 223
REMOVED: B VII Probability theory
pp. 223
Appendix
pp. 224
45. Titchmarsh Convolution Theorem
pp. 225
Chapter 13 Three Colors
pp. 225
Appendix B Map Spaces
pp. 225
Chapter 15 Organizing a Program Library
pp. 226
Chapter 11 Zeros on the line
pp. 226
Chapter VI Abstract Class Field Theory
pp. 227
46. The Spectrum of a Distribution
pp. 227
VIII Orlicz and Orlicz-Sobolev Spaces
pp. 229
Chapter 16 Algebra
pp. 230
Chapter V Analytic Sets
pp. 231
REMOVED: C I Categories and sheaves
pp. 231
V Several Finite Substitutions Iterated
pp. 233
Bibliography
pp. 233
Chapter 12 Applications
pp. 236
47. Tauberian Theorems
pp. 239
Chapter 14 Edge Coloration
pp. 239
Appendix C The Contraction Mapping Theorem
pp. 241
48. Prime Number Theorem
pp. 241
Index
pp. 244
Chapter VII Groups of Transformations of Kaehler and Almost Kaehler Manifolds
pp. 246
49. The Riemann Zeta Function
pp. 246
Bibliography
pp. 249
Bibliography
pp. 249
REMOVED: C II Commutative algebra
pp. 252
50. Beurling's Theorem
pp. 252
Bibliography
pp. 252
IV Integration in Spaces of More Than One Dimension
pp. 253
Index
pp. 253
Chapter V Theory of Convergence
pp. 255
Author Index
pp. 257
51. Riesz Convexity Theorem
pp. 257
Subject Index
pp. 257
Chapter IV The Axiomatic Structure of Quantum Mechanics
pp. 257
Chapter 7 Computing Stable Homotopy Groups with the Adams-Novikov Spectral Sequence
pp. 260
Chapter 12 Miscellany
pp. 260
Reference
pp. 261
REMOVED: C III Spectral theory of operators
pp. 263
52. The Salem Example
pp. 265
Index
pp. 265
51-62 Reality in Lie Groups and Algebras and their Linear Representations
pp. 267
References
pp. 269
Index
pp. 270
Appendix A De Rham's Theorems
pp. 271
Subject Index
pp. 271
53. Convolution Operators
pp. 273
REMOVED: Bibliography
pp. 276
Index of Notations
pp. 278
54. A Hardy-Littlewood Inequality
pp. 280
VI Other Topics: An Overview
pp. 281
Chapter 17 Analysis
pp. 283
REMOVED: Index
pp. 285
The Lorentz Group and Its Representations
pp. 285
55. Functions of Exponential Type
pp. 292
56. The Bessel Kernel
pp. 293
Appendix B The Cup Product
pp. 295
Chapter 5 Measurable Cardinals
pp. 296
Appendix C The Hodge Existence Theorem
pp. 297
57. The Bessel Potential
pp. 299
Appendix on the Number of Primes Less Than a Given Magnitude
pp. 301
Appendix D Partition of Unity
pp. 303
References
pp. 306
References
pp. 306
Appendix 1 Hopf Algebras and Hopf Algebroids
pp. 306
58. The Spaces of Bessel Potentials
pp. 307
Author Index
pp. 309
Author Index
pp. 309
Subject Index
pp. 311
Index
pp. 311
Subject Index
pp. 313
Index
pp. 321
Representations of the Classical Groups
pp. 323
Chapter 18 Arithmetic
pp. 333
Chapter 19 Asymptotics
pp. 337
Historical and Bibliographical Remarks
pp. 341
References
pp. 349
Index
pp. 349
63-67 Symmetric Spaces
pp. 354
Appendix 2 Formal Group Laws
pp. 355
Chapter 20 Geometry
pp. 357
Chapter VI Language of Sheaves
pp. 363
V Line Integrals and Areas of Surfaces
pp. 380
Appendix 3 Tables of Homotopy Groups of Spheres
pp. 382
Chapter 21 Graphs
pp. 391
Chapter 22 Probability
pp. 394
Chapter VII Analytic Spaces
pp. 395
68-75 Tits Geometries
pp. 395
References
pp. 397
The Harmonic Oscillator Group
pp. 398
Chapter 6 Other Large Cardinals
pp. 407
Hilbert Space
pp. 407
Index
pp. 414
Chapter V Quantum Mechanical Scattering Theory
pp. 415
References
pp. 421
Symbol Index
pp. 425
Index
pp. 438
VI Vector Spaces, Orthogonal Expansions, and Fourier Transforms
pp. 440
Chapter 23 Special Functions
pp. 451
Chapter 24 Statistics
pp. 471
Bibliography
pp. 475
Index of Notation
pp. 479
Subject Index
pp. 484
Chapter 25 Utilities
pp. 493
Chapter 7 Descriptive Set Theory
pp. 497
76-77 Betti Numbers of Semisimple Lie Groups and Regular Subalgebras of Semisimple Lie Algebras
pp. 498
References
pp. 502
Solutions to Exercises
pp. 519
Index
pp. 527
Appendix
pp. 535
VII Measure Theory
pp. 539
Key to Definitions
pp. 547
Author Index
pp. 579
Historical Notes And Guide To The Bibliography
pp. 596
Bibliography
pp. 603
Index
pp. 611
Notation
pp. 615
Index
pp. 631
Hints and Solutions to Exercises
pp. 669
References
pp. 679
Index
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