Singularities and groups in bifurcation theory.

Title list......Page gol1.djvu
Preface......Page gol1_0004.djvu
Contents......Page gol1_0011.djvu
§0. Introduction......Page gol1_0014.djvu
§1. The Pitchfork Bifurcation......Page gol1_0015.djvu
§2. The Continuous Flow Stirred Tank Reactor (CSTR)......Page gol1_0029.djvu
§3. A First View of the Liapunov-Schmidt Reduction......Page gol1_0038.djvu
§4. Asymptotic Stability and the Liapunov-Schmidt Reduction......Page gol1_0048.djvu
APPENDIX 1 The Implicit Function Theorem......Page gol1_0057.djvu
APPENDIX 2 Equivalence and the Liapunov-Schmidt Reduction......Page gol1_0060.djvu
§0. Introduction......Page gol1_0064.djvu
§1. Germs: A Preliminary Issue......Page gol1_0067.djvu
§2. The Restricted Tangent Space......Page gol1_0069.djvu
§3. Calculation of RT(g), I: Simple Examples......Page gol1_0071.djvu
§4. Principles for Calculating RT{g), I: Basic Algebra......Page gol1_0076.djvu
§5. Principles for Calculating RT(g), II: Finite Determinacy......Page gol1_0079.djvu
§6. Calculation of RT(g), II: A Hard Example......Page gol1_0090.djvu
§7. Principles for Calculating RT(g), III: Intrinsic Ideals......Page gol1_0094.djvu
§8. Formulation of the Main Results......Page gol1_0099.djvu
§9. Solution of the Recognition Problem for Several Examples......Page gol1_0106.djvu
§10. The Recognition Problem: General Equivalences......Page gol1_0109.djvu
§11. Proof of Theorem 2.2......Page gol1_0111.djvu
§12. Proof of Proposition 8.6(b)......Page gol1_0115.djvu
§13. Proof of Theorem 8.7......Page gol1_0120.djvu
§0. Introduction......Page gol1_0130.djvu
§1. Unfoldings and Universal Unfoldings......Page gol1_0133.djvu
§2. A Characterization of Universal Unfoldings......Page gol1_0136.djvu
§3. Examples of Universal Unfoldings......Page gol1_0142.djvu
§4. The Recognition Problem for Universal Unfoldings......Page gol1_0146.djvu
§5. Nonpersistent Bifurcation Diagrams......Page gol1_0153.djvu
§6. Statement of the Main Geometric Theorem......Page gol1_0156.djvu
§7. A Simple Example: The Pitchfork......Page gol1_0158.djvu
§8. A Complicated Example: The Winged Cusp......Page gol1_0161.djvu
§9. A Sketch of the Proof of Theorem 6.1......Page gol1_0165.djvu
§10. Persistence on a Bounded Domain in a Parametrized Family......Page gol1_0167.djvu
§11. The Proof of Theorem 10.1......Page gol1_0172.djvu
§12. The Path Formulation......Page gol1_0178.djvu
CASE STUDY 1 The CSTR......Page gol1_0187.djvu
§0. Introduction......Page gol1_0195.djvu
§1. Philosophical Remarks Concerning Codimension......Page gol1_0196.djvu
§2. The Classification Theorem......Page gol1_0209.djvu
§3. Universal Unfoldings of the Elementary Bifurcations......Page gol1_0215.djvu
§4. Transition Varieties and Persistent Diagrams......Page gol1_0218.djvu
§0. Introduction......Page gol1_0226.djvu
§1. The Problem of Moduli: Smooth Versus Topological Equivalence......Page gol1_0227.djvu
§2. The Recognition Problem for Nondegenerate Cubics......Page gol1_0229.djvu
§3. Universal Unfolding; Relation to Moduli......Page gol1_0232.djvu
§4. Persistent Perturbed Diagrams......Page gol1_0235.djvu
§5. A Picture of the Moduli Family......Page gol1_0239.djvu
§6. Discussion of Moduli and Topological Codimension......Page gol1_0249.djvu
§7. The Thermal-Chainbranching Model......Page gol1_0252.djvu
§0. Introduction......Page gol1_0256.djvu
§1. A Simple Physical Example with Z_2-Symmetry......Page gol1_0257.djvu
§2. The Recognition Problem......Page gol1_0260.djvu
§3. Universal Unfoldings......Page gol1_0270.djvu
§4. Persistent Perturbations......Page gol1_0273.djvu
§5. The Z_2-Classification Theorem......Page gol1_0276.djvu
§6. Persistent Perturbations of the Nonmodal Bifurcations......Page gol1_0280.djvu
§7. The Unimodal Family of Codimension Three......Page gol1_0285.djvu
§8. Perturbations at the Connector Points......Page gol1_0293.djvu
§0. Introduction......Page gol1_0302.djvu
§1. The Liapunov-Schmidt Reduction Without Symmetry......Page gol1_0303.djvu
§2. The Elastica: An Example in Infinite Dimensions......Page gol1_0309.djvu
§3. The Liapunov-Schmidt Reduction with Symmetry......Page gol1_0313.djvu
§4. The Liapunov-Schmidt Reduction of Scalar Reaction-Diffusion Equations......Page gol1_0321.djvu
§5. The Brusselator......Page gol1_0325.djvu
§6. The Liapunov-Schmidt Reduction of the Brusselator......Page gol1_0330.djvu
APPENDIX 3 Smooth Mappings Between Banach Spaces......Page gol1_0342.djvu
APPENDIX 4 Some Properties of Linear Elliptic Differential Operators......Page gol1_0345.djvu
§0. Introduction......Page gol1_0350.djvu
§1. Simple Examples of Hopf Bifurcation......Page gol1_0351.djvu
§2. Finding Periodic Solutions by a Liapunov-Schmidt Reduction......Page gol1_0354.djvu
§3. Existence and Uniqueness of Solutions......Page gol1_0363.djvu
§4. Exchange of Stability......Page gol1_0371.djvu
§5. Degenerate Hopf Bifurcation......Page gol1_0385.djvu
CASE STUDY 2 The Clamped Hodgkin-Huxley Equations......Page gol1_0395.djvu
§0. Introduction......Page gol1_0410.djvu
§1. Bifurcation with n State Variables......Page gol1_0411.djvu
§2. Hilltop Bifurcation......Page gol1_0413.djvu
§3. Persistent Bifurcation Diagrams for Hilltop Bifurcation......Page gol1_0420.djvu
§0. Introduction......Page gol1_0430.djvu
§1. Bifurcation Problems with (Z_2  oplus  Z_2)-Symmetry......Page gol1_0431.djvu
§2. Singularity Theory Results......Page gol1_0434.djvu
§3. Linearized Stability and (Z_2  oplus  Z_2)-Symmetry......Page gol1_0439.djvu
§4. The Bifurcation Diagrams for Nondegenerate Problems......Page gol1_0443.djvu
CASE STUDY 3 Mode Jumping in the Buckling of a Rectangular Plate......Page gol1_0452.djvu
Bibliography......Page gol1_0467.djvu
Symbol Index......Page gol1_0472.djvu
Index......Page gol1_0473.djvu