Author | Berger, Melvyn S. author |
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Title | Mathematical Structures of Nonlinear Science [electronic resource] : An Introduction / by Melvyn S. Berger |
Imprint | Dordrecht : Springer Netherlands, 1990 |
Connect to | http://dx.doi.org/10.1007/978-94-009-0579-5 |
Descript | 430 p. online resource |
1 Integrable Nonlinear Systems and their Perturbation -- 1.1 The Simplest Nonlinear Systems -- 1.2 Integration by Quadrature and Its Alternatives -- 1.3 Classical Mechanical Integrable Systems -- 1.4 New Ideas on Complete Integrability for Equilibrium Processes -- 1.5 Canonical Changes of Coordinates for the Mapping A -- 1.6 Bifurcation and the Integration of Nonlinear Ordinary and Partial Differential Equations -- 1.7 Qualitative Properties of Integrable Systems โ Periodic and Quasiperiodic Motions of Dynamical Systems -- 1.8 Almost Periodic Motions of Dynamical Systems -- Appendix 1 Nonlinear Fredholm Operators -- Appendix 2 Bifurcation from Equilibria for Certain Infinite-Dimensional Dynamical Systems -- Appendix 3 Elementary Facts about the Linear Dirichlet Problem -- Appendix 4 On Besicovitch Almost Periodic Functions -- 2 General Principles for Nonlinear Systems -- 2.1 Differentiable Nonlinear Operators -- 2.2 Iteration of Nonlinear Operators -- 2.3 Nonlinear Fredholm Alternatives -- 2.4 The Idea of Nonlinear Desingularization -- 2.5 Variational Principles โ New Ideas in the Calculus of Variations in the Large -- 2.6 Bifurcation -- 2.7 Bifurcation Into Folds -- 3 Some Connections between Global Differential Geometry and Nonlinear Analysis -- 3.1 Geodesics -- 3.2 Gauss Curvature and Its Extensions -- 3.3 Manifolds of Constant Gauss Positive Curvature -- 3.4 Mean Curvature -- 3.5 Simple Riemannian Metrics -- 3.6 Einstein Metrics -- 4 Vortices in Ideal Fluids -- 4.1 The Early History of Vortices in Fluids -- 4.2 Formulation of the Vortex Concept in Ideal Incompressible Fluids -- 4.3 Axisymmetric Vortex Motions with and without Swirl -- 4.4 Variational Principles for the Stream Function for Vortex Rings without Swirl -- 4.5 Leapfrogging of Vortices -- 4.6 Vortex Breakdown -- 4.7 Nonlinear Desingularization and Vortex Filaments -- 5 Mathematical Aspects of Superconductivity -- 5.1 The Simplest Nonlinear Yang-Mills Theory that Works -- 5.2 Physical Viewpoint -- 5.3 The Linear Approach to Superconductivity and Nonlinear Desingularization -- 5.4 Function Spaces for Symmetric Vortices -- 5.5 The Existence of Critical Points for I? Associated with Symmetric Vortices -- Problems