Attractors of Hamiltonian Nonlinear Partial Differential Equations

Contents
Preface
Introduction
1. Global Attraction to Stationary States
	1.1 Free d’Alembert Equation
	1.2 A String Coupled to a Nonlinear Oscillator
	1.3 String Coupled to Several Nonlinear Oscillators
	1.4 Space-Localized Nonlinearity
	1.5 Wave–Particle System
	1.6 Maxwell-Lorentz Equations: Radiation Damping
	1.7 Wave Equations with Concentrated Nonlinearities
	1.8 Comparison with Dissipative Systems
2. Global Attraction to Solitons
	2.1 Translation-InvariantWave–Particle System
	2.2 The Case of Weak Coupling
3. Global Attraction to Stationary Orbits
	3.1 Nonlinear Klein–Gordon Equation
	3.2 Generalizations and Open Questions
	3.3 Omega-Limit Trajectories
	3.4 Limiting Absorption Principle
	3.5 A Nonlinear Analog of Kato’s Theorem
	3.6 Splitting into Dispersive and Bound Components
	3.7 Omega-Compactness
	3.8 Reduction of Spectrum to Spectral Gap
	3.9 Reduction of Spectrum to a Single Point
	3.10 On the Nonlinear Radiative Mechanism
	3.11 Conjecture on Attractors of G-Invariant PDEs
4. Asymptotic Stability of Stationary Orbits and Solitons
	4.1 Orthogonal Projection
	4.2 Symplectic Projection
	4.3 Generalizations and Applications
	4.4 Further Generalizations
	4.5 The 1D Schrödinger Equation Coupled to an Oscillator
5. Adiabatic Effective Dynamics of Solitons
	5.1 Solitons in Slowly Varying External Potentials
	5.2 Mass–Energy Equivalence
6. Numerical Simulation of Solitons
	6.1 Kinks of Relativistic Equations
	6.2 Numerical Observation of Soliton Asymptotics
	6.3 Adiabatic Effective Dynamics of Relativistic Solitons
7. Dispersive Decay
	7.1 The Schrödinger and Klein–Gordon Equations
	7.2 Decay L1 L^∞ for 3D Schrödinger Equations
8. Attractors and Quantum Mechanics
	8.1 Bohr’s Postulates
	8.2 On Dynamical Interpretation of Quantum Jumps
	8.3 Bohr’s Postulates via Perturbation Theory
	8.4 Conclusion
Bibliography
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Index
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