Singularities and groups in bifurcation theory.

Title list......Page gol2.djvu
Preface......Page gol2_0004.djvu
Contents......Page gol2_0006.djvu
Contents of Volume I......Page gol2_0010.djvu
§0. Introduction......Page gol2_0014.djvu
§1. Equations with Symmetry......Page gol2_0015.djvu
§2. Techniques......Page gol2_0022.djvu
§3. Mode Interactions......Page gol2_0031.djvu
§4. Overview......Page gol2_0034.djvu
§0. Introduction......Page gol2_0036.djvu
§1. Group Theory......Page gol2_0038.djvu
§2. Irreducibility......Page gol2_0046.djvu
§3. Commuting Linear Mappings and Absolute Irreducibility......Page gol2_0052.djvu
§4. Invariant Functions......Page gol2_0056.djvu
§5. Nonlinear Commuting Mappings......Page gol2_0062.djvu
§6.* Proofs of Theorems in §§4 and 5......Page gol2_0067.djvu
§7.* Tori......Page gol2_0076.djvu
§0. Introduction......Page gol2_0080.djvu
§1. Orbits and Isotropy Subgroups......Page gol2_0082.djvu
§2. Fixed-Point Subspaces and the Trace Formula......Page gol2_0086.djvu
§3. The Equivariant Branching Lemma......Page gol2_0093.djvu
§4. Orbital Asymptotic Stability......Page gol2_0099.djvu
§5. Bifurcation Diagrams and Dn Symmetry......Page gol2_0108.djvu
§6.† Subgroups of SO(3)......Page gol2_0116.djvu
§7.† Representations of SO (3) and O (3): Spherical Harmonics......Page gol2_0120.djvu
§8.† Symmetry-Breaking from SO(3)......Page gol2_0128.djvu
§9.† Symmetry-Breaking from 0(3)......Page gol2_0132.djvu
§10.* Generic Spontaneous Symmetry-Breaking......Page gol2_0145.djvu
§0. Introduction......Page gol2_0154.djvu
§1. Discussion of the PDE......Page gol2_0161.djvu
§2. One-Dimensional Fixed-Point Subspaces......Page gol2_0166.djvu
§3. Bifurcation Diagrams and Asymptotic Stability......Page gol2_0169.djvu
§0. Introduction......Page gol2_0177.djvu
§1. The Recognition Problem......Page gol2_0178.djvu
§2.* Proof of Theorem 1.3......Page gol2_0185.djvu
§3. Sample Computations of RT(h,Gamma)......Page gol2_0189.djvu
§4. Sample Recognition Problems......Page gol2_0198.djvu
§5. Linearized Stability and Gamma-equivalence......Page gol2_0212.djvu
§6. Intrinsic Ideals and Intrinsic Submodules......Page gol2_0215.djvu
§7. Higher Order Terms......Page gol2_0217.djvu
§0. Introduction......Page gol2_0221.djvu
§1. Basic Definitions......Page gol2_0222.djvu
§2. The Equivariant Universal Unfolding Theorem......Page gol2_0223.djvu
§3. Sample Universal Gamma-unfoldings......Page gol2_0226.djvu
§4. Bifurcation with D_3 Symmetry......Page gol2_0231.djvu
§5.† The Spherical Bénard Problem......Page gol2_0236.djvu
§6.† Spherical Harmonics of Order 2......Page gol2_0240.djvu
§7.* Proof of the Equivariant Universal Unfolding Theorem......Page gol2_0246.djvu
§8.* The Equivariant Preparation Theorem......Page gol2_0256.djvu
§0. Introduction......Page gol2_0260.djvu
§1. Reduction to D_3 Symmetry in the Plane......Page gol2_0263.djvu
§2. Taylor Coefficients in the Bifurcation Equation......Page gol2_0264.djvu
§3. Bifurcations of the Rivlin Cube......Page gol2_0268.djvu
§0. Introduction......Page gol2_0271.djvu
§1. Conditions for Imaginary Eigenvalues......Page gol2_0274.djvu
§2. A Simple Hopf Theorem with Symmetry......Page gol2_0280.djvu
§3. The Circle Group Action......Page gol2_0282.djvu
§4. The Hopf Theorem with Symmetry......Page gol2_0288.djvu
§5. Birkhoff Normal Form and Symmetry......Page gol2_0297.djvu
§6. Floquet Theory and Asymptotic Stability......Page gol2_0306.djvu
§7. Isotropy Subgroups of Gamma x S^1......Page gol2_0312.djvu
§8.* Dimensions of Fixed-Point Subspaces......Page gol2_0315.djvu
§9. Invariant Theory for Gamma x S^1......Page gol2_0321.djvu
§10. Relationship Between Liapunov-Schmidt Reduction and Birkhoff Normal Form......Page gol2_0323.djvu
§11.* Stability in Truncated Birkhoff Normal Form......Page gol2_0326.djvu
§0. Introduction......Page gol2_0337.djvu
§1. The Action of 0(2) x S^1......Page gol2_0338.djvu
§2. Invariant Theory for 0(2) x S^1......Page gol2_0344.djvu
§3. The Branching Equations......Page gol2_0345.djvu
§4. Amplitude Equations, D_4 Symmetry, and Stability......Page gol2_0346.djvu
§5.t Hopf Bifurcation with 0(n) Symmetry......Page gol2_0351.djvu
§6.† Bifurcation with D_4 Symmetry......Page gol2_0354.djvu
§7. The Bifurcation Diagrams......Page gol2_0361.djvu
§8.† Rotating Waves and SO(2) or Z_n Symmetry......Page gol2_0372.djvu
§0. Introduction......Page gol2_0376.djvu
§1. The Action of D_n x S^1......Page gol2_0380.djvu
§2. Invariant Theory for D_n x S^1......Page gol2_0385.djvu
§3. Branching and Stability for D_n......Page gol2_0389.djvu
§4. Oscillations of Identical Cells Coupled in a Ring......Page gol2_0400.djvu
§5.† Hopf Bifurcation with 0(3) Symmetry......Page gol2_0412.djvu
§6.† Hopf Bifurcation on the Hexagonal Lattice......Page gol2_0416.djvu
§0. Introduction......Page gol2_0425.djvu
§1. Hopf/Steady-State Interaction......Page gol2_0429.djvu
§2. Bifurcation Problems with Z_2 Symmetry......Page gol2_0430.djvu
§3. Bifurcation Diagrams with Z_2 Symmetry......Page gol2_0438.djvu
§4. Hopf/Hopf Interaction......Page gol2_0455.djvu
§0. Introduction......Page gol2_0459.djvu
§l.† Steady-State Mode Interaction......Page gol2_0461.djvu
§2. Hopf/Steady-State Mode Interaction......Page gol2_0471.djvu
§3.† Hopf/Hopf Mode Interaction......Page gol2_0488.djvu
§0. Introduction......Page gol2_0498.djvu
§1. Detailed Overview......Page gol2_0499.djvu
§2. The Bifurcation Theory Analysis......Page gol2_0511.djvu
§3. Finite Length Effects......Page gol2_0522.djvu
Bibliography......Page gol2_0526.djvu
Index......Page gol2_0540.djvu