Singularities and Groups in Bifurcation Theory Volume II - neues Buch

EAN (ISBN-13): 9781461289296
ISBN (ISBN-10): 1461289297
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2012
Herausgeber: Springer

Buch in der Datenbank seit 2012-12-02T23:40:49+01:00 (Berlin)
Detailseite zuletzt geändert am 2024-03-20T08:23:20+01:00 (Berlin)
ISBN/EAN: 9781461289296

ISBN - alternative Schreibweisen:
1-4612-8929-7, 978-1-4612-8929-6
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: schaeffer, stewart david, ian, martin, golub
Titel des Buches: singularities and groups bifurcation theory, group theory, bifur, singularities volume

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Daten vom Verlag:

Autor/in: Martin Golubitsky; Ian Stewart; David G. Schaeffer
Titel: Applied Mathematical Sciences; Singularities and Groups in Bifurcation Theory - Volume II
Verlag: Springer; Springer US
536 Seiten
Erscheinungsjahr: 2011-10-08
New York; NY; US
Gedruckt / Hergestellt in Niederlande.
Sprache: Englisch
192,59 € (DE)
197,99 € (AT)
212,50 CHF (CH)
POD
XVI, 536 p.

BC; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Gruppen und Gruppentheorie; Verstehen; Group theory; Irreducibility; Lattice; group action; invariant theory; partial differential equation; Group Theory and Generalizations; BB

of Volume II.- XI Introduction.- §0. Introduction.- §1. Equations with Symmetry.- §2. Techniques.- §3. Mode Interactions.- §4. Overview.- XII Group-Theoretic Preliminaries.- §0. Introduction.- §1. Group Theory.- §2. Irreducibility.- §3. Commuting Linear Mappings and Absolute Irreducibility.- §4. Invariant Functions.- §5. Nonlinear Commuting Mappings.- §6.* Proofs of Theorems in §§4 and 5.- §7.* Tori.- XIII Symmetry-Breaking in Steady-State Bifurcation.- §0. Introduction.- §1. Orbits and Isotropy Subgroups.- §2. Fixed-Point Subspaces and the Trace Formula.- §3. The Equivariant Branching Lemma.- §4. Orbital Asymptotic Stability.- §5. Bifurcation Diagrams and DnSymmetry.- §6.† Subgroups of SO(3).- §7.† Representations of SO(3) and O(3): Spherical Harmonics.- §8.† Symmetry-Breaking from SO(3).- §9.† Symmetry-Breaking from O(3).- §10.* Generic Spontaneous Symmetry-Breaking.- Case Study 4 The Planar Bénard Problem.- §0. Introduction.- §1. Discussion of the PDE.- §2. One-Dimensional Fixed-Point Subspaces.- §3. Bifurcation Diagrams and Asymptotic Stability.- XIV Equivariant Normal Forms.- §0. Introduction.- §1. The Recognition Problem.- §2.* Proof of Theorem 1.3.- §3. Sample Computations of RT(h, ?).- §4. Sample Recognition Problems.- §5. Linearized Stability and ?-equivalence.- §6. Intrinsic Ideals and Intrinsic Submodules.- §7. Higher Order Terms.- XV Equivariant Unfolding Theory.- §0. Introduction.- §1. Basic Definitions.- §2. The Equivariant Universal Unfolding Theorem.- §3. Sample Universal ?-unfoldings.- §4. Bifurcation with D3 Symmetry.- §5.† The Spherical Bénard Problem.- §6.† Spherical Harmonics of Order 2.- §7.* Proof of the Equivariant Universal Unfolding Theorem.- §8.* The Equivariant PreparationTheorem.- Case Study 5 The Traction Problem for Mooney-Rivlin Material.- §0. Introduction.- §1. Reduction to D3 Symmetry in the Plane.- §2. Taylor Coefficients in the Bifurcation Equation.- §3. Bifurcations of the Rivlin Cube.- XVI Symmetry-Breaking in Hopf Bifurcation.- §0. Introduction.- §1. Conditions for Imaginary Eigenvalues.- §2. A Simple Hopf Theorem with Symmetry.- §3. The Circle Group Action.- §4. The Hopf Theorem with Symmetry.- §5. Birkhoff Normal Form and Symmetry.- §6. Floquet Theory and Asymptotic Stability.- §7. Isotropy Subgroups of ? × S1.- §8.* Dimensions of Fixed-Point Subspaces.- §9. Invariant Theory for ? × S1.- 10. Relationship Between Liapunov-Schmidt Reduction and Birkhoff Normal Form.- §11.* Stability in Truncated Birkhoff Normal Form.- XVII Hopf Bifurcation with O(2) Symmetry.- §0. Introduction.- §1. The Action of O(2) × S1.- §2. Invariant Theory for O(2) × S1.- §3. The Branching Equations.- §4. Amplitude Equations, D4 Symmetry, and Stability.- §5.† Hopf Bifurcation with O(n) Symmetry.- §6.† Bifurcation with D4 Symmetry.- §7. The Bifurcation Diagrams.- §8.† Rotating Waves and SO(2) or Zn Symmetry.- XVIII Further Examples of Hopf Bifurcation with Symmetry.- §0. Introduction.- §1. The Action of Dn × S1.- §2. Invariant Theory for Dn × S1.- §3. Branching and Stability for Dn.- §4. Oscillations of Identical Cells Coupled in a Ring.- §5.† Hopf Bifurcation with O(3) Symmetry.- §6.† Hopf Bifurcation on the Hexagonal Lattice.- XIX Mode Interactions.- §0. Introduction.- § 1. Hopf/Steady-State Interaction.- §2. Bifurcation Problems with Z2 Symmetry.- §3. Bifurcation Diagrams with Z2 Symmetry.- §4. Hopf/Hopf Interaction.- XX Mode Interactions with O(2) Symmetry.- §0. Introduction.- §l.†Steady-State Mode Interaction.- §2. Hopf/Steady-State Mode Interaction.- §3.† Hopf/Hopf Mode Interaction.- Case Study 6 The Taylor-Couette System.- §0. Introduction.- §1. Detailed Overview.- §2. The Bifurcation Theory Analysis.- §3. Finite Length Effects.