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1.

図書

図書
édité par Gérard Iooss, Robert H.G. Helleman, Raymond Stora
出版情報: Amsterdam ; New York : North-Holland Pub. Co. , New York, N.Y. : Sole distributors for the USA and Canada, Elsevier Science Pub. Co., 1983  xxxi, 708 p., [1] leaf of plates ; 23 cm
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2.

図書

図書
edited by G.I. Barenblatt, G. Iooss, D.D. Joseph
出版情報: Boston : Pitman Advanced Pub. Program, 1983  xvi, 356 p. ; 24 cm
シリーズ名: Interaction of mechanics and mathematics series
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3.

図書

図書
Gérard Iooss, Daniel D. Joseph
出版情報: New York : Springer-Verlag, c1980  xv, 286 p. ; 24 cm
シリーズ名: Undergraduate texts in mathematics
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目次情報: 続きを見る
Asymptotic Solutions of Evolution Problems
Bifurcation and Stability of Steady Solutions of Evolution Equations in One Dimension
Imperfection Theory and Isolated Solutions Which Perturb Bifurcation
Stability of Steady Solutions of Evolution Equations in Two Dimensions and n Dimensions. Appendices
Bifurcation of Steady Solution in Two Dimensions and the Stability of the Bifurcating Solutions. Appendix
Methods of Projection for General Problems of Bifurcation into Steady Solutions
Bifurcation of Periodic Solutions from Steady Ones (Hopf Bifurcation) in Two Dimensions
Bifurcation of Periodic Solutions in the General Case
Subharmonic Bifurcation of Forced T-Periodic Solutions
Bifurcation of Forced T-Periodic Solutions into Asymptotically Quasi-Periodic Solutions. Appendices
Secondary Subharmonic and Symptotically Quasi-Periodic Bifurcation of Periodic Solutions (of Hopf's Type) in the Autonomous Case
Stability and Bifurcation in Conservative Systems
Asymptotic Solutions of Evolution Problems
Bifurcation and Stability of Steady Solutions of Evolution Equations in One Dimension
Imperfection Theory and Isolated Solutions Which Perturb Bifurcation
4.

図書

図書
Pascal Chossat, Gérard Iooss
出版情報: New York : Springer-Verlag, c1994  ix, 233 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 102
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5.

図書

図書
Gérard Iooss, Daniel D. Joseph
出版情報: New York ; Tokyo : Springer-Verlag, c1990  xxiii, 324 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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目次情報: 続きを見る
Asymptotic Solutions of Evolution Problems
Bifurcation and Stability of Steady Solutions of Evolution Equations in One Dimension
Imperfection Theory and Isolated Solutions Which Perturb Bifurcation
Stability of Steady Solutions of Evolution Equations in Two Dimensions and n Dimensions. Appendices
Bifurcation of Steady Solution in Two Dimensions and the Stability of the Bifurcating Solutions. Appendix
Methods of Projection for General Problems of Bifurcation into Steady Solutions
Bifurcation of Periodic Solutions from Steady Ones (Hopf Bifurcation) in Two Dimensions
Bifurcation of Periodic Solutions in the General Case
Subharmonic Bifurcation of Forced T-Periodic Solutions
Bifurcation of Forced T-Periodic Solutions into Asymptotically Quasi-Periodic Solutions. Appendices
Secondary Subharmonic and Symptotically Quasi-Periodic Bifurcation of Periodic Solutions (of Hopf's Type) in the Autonomous Case
Stability and Bifurcation in Conservative Systems
Asymptotic Solutions of Evolution Problems
Bifurcation and Stability of Steady Solutions of Evolution Equations in One Dimension
Imperfection Theory and Isolated Solutions Which Perturb Bifurcation
6.

電子ブック

EB
Mariana Haragus, Gérard Iooss, Gérard Iooss
出版情報: SpringerLink Books Mathematics And Statistics 2011 , Springer London, 2011
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目次情報: 続きを見る
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:
Bénard-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:
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