Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems

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Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems / Mariana Haragus, Gérard Iooss, Gérard Iooss

資料種別:

電子ブック

出版情報:

SpringerLink Books - AutoHoldings
Springer London, 2011

著者名:

ISBN:

9780857291110 [0857291114]
9780857291127 [0857291122]

書誌ID:

OB00498431

子書誌情報

フルテキスト

所蔵情報

書誌詳細

その他の標題:

UNIVERSITEXT

言語:

英語

目次情報:

Elementary Bifurcations / 1：

Bifurcations in Dimension 1 / 1.1：

Saddle-Node Bifurcation / 1.1.1：

Pitchfork Bifurcation / 1.1.2：

Bifurcations in Dimension 2 / 1.2：

Hopf Bifurcation / 1.2.1：

Example: Homogeneous Brusselator / 1.2.2：

Hopf Bifurcation with SO(2) Symmetry / 1.2.3：

Steady Bifurcation with O(2) Symmetry / 1.2.4：

Center Manifolds / 2：

Notations / 2.1：

Local Center Manifolds / 2.2：

Hypotheses / 2.2.1：

Main Result / 2.2.2：

Checking Hypothesis 2.7 / 2.2.3：

Examples / 2.2.4：

Particular Cases and Extensions / 2.3：

Parameter-Dependent Center Manifolds / 2.3.1：

Nonautonomous Center Manifolds / 2.3.2：

Symmetries and Reversibility / 2.3.3：

Empty Unstable Spectrum / 2.3.4：

Further Examples and Exercises / 2.4：

A Fourth Order ODE / 2.4.1：

Burgers Model / 2.4.2：

Swift-Hohenberg Equation / 2.4.3：

Brusselator Model / 2.4.4：

Elliptic PDE in a Strip / 2.4.5：

Normal Forms / 3：

Main Theorem / 3.1：

Proof of Theorem 1.2 / 3.1.1：

Parameter-Dependent Normal Forms / 3.1.2：

Linear Normal Forms / 3.2.1：

Derivation of the Parameter-Dependent Normal Form / 3.2.3：

Equivariant Vector Fields / 3.2.4：

Reversible Vector Fields / 3.3.2：

Example: van der Pol System / 3.3.3：

Normal Forms for Reduced Systems on Center Manifolds / 3.4：

Computation of Center Manifolds and Normal Forms / 3.4.1：

Example 1: Hopf Bifurcation / 3.4.2：

Example 2: Hopf Bifurcations with Symmetries / 3.4.3：

Example 3: Takens-Bogdanov Bifurcation / 3.4.4：

Further Normal Forms / 3.4.5：

Time-Periodic Normal Forms / 3.5.1：

Example: Periodically Forced Hopf Bifurcation / 3.5.2：

Normal Forms for Analytic Vector Fields / 3.5.3：

Reversible Bifurcations / 4：

Dimension 2 / 4.1：

Dimension 3 / 4.1.1：

Reversible 0(i?) Bifurcation (Elements) / 4.2.1：

Dimension 4 / 4.3：

Applications / 4.3.1：

Hydrodynamic Instabilities / 5.1：

Hydrodynamic Problem / 5.1.1：

Couette-Taylor Problem / 5.1.2：

BÃ©nard-Rayleigh Convection Problem / 5.1.3：

Existence of Traveling Waves / 5.2：

Gravity-Capillary Water-Waves / 5.2.1：

Almost-Planar Waves in Reaction-Diffusion Systems / 5.2.2：

Waves in Lattices / 5.2.3：

Appendix

Elements of Functional Analysis / A：

Bounded and Closed Operators / A.1：

Resolvent and Spectrum / A.2：

Compact Operators and Operators with Compact Resolvent / A.3：

Adjoint Operator / A.4：

Fredholm Operators / A.5：

Basic Sobolev Spaces / A.6：

Proof of Theorem 2.9 (Center Manifolds) / B：

Proof of Theorem 2.17 (Semilinear Case) / B.2：

Proof of Theorem 3.9 (Nonautonomous Vector Fields) / B.3：

Proof of Theorem 3.13 (Equivariant Systems) / B.4：

Proof of Theorem 3.22 (Empty Unstable Spectrum) / B.5：

Proof of Theorem 2.2 (Perturbed Normal Forms) / C：

References / D：

Index

Elementary Bifurcations / 1：

Bifurcations in Dimension 1 / 1.1：

Saddle-Node Bifurcation / 1.1.1：

Pitchfork Bifurcation / 1.1.2：

Bifurcations in Dimension 2 / 1.2：

Hopf Bifurcation / 1.2.1：

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