Contents
1. Introduction
1.1. Non-Technical Description
1.2. Mathematical Formulation
1.3. About this Thesis
2. Mathematical Tools
2.1. Basic Analysis
2.2. Ordinary Differential Equations
2.3. Dynamical Systems
2.4. Normal Forms and Bifurcations
2.A. Some Important Functions
3. Physical Models
3.1. Damped Particle in a Potential
3.2. Magnets at Equilibrium
3.3. Magnets out of Equilibrium
3.4. Phenomenological Models of Hysteresis
4. One-Dimensional Systems
4.1. Preliminaries
4.2. Adiabatic Solutions
4.3. Bifurcations: Real Case
4.4. Bifurcations: Complex Case
4.5. Global Properties of the Flow
4.6. Periodic Systems and Hysteresis
4.7. Summary and Conclusion
4.A. Proofs of Some Results
5. n-Dimensional Systems
5.1. Preliminaries
5.2. Adiabatic Solutions
5.3. Linear Systems
5.4. Effect of Nonlinear Terms
5.5. Periodic Systems and Hysteresis
5.6. Summary and Conclusion
5.A. Some Properties of Matrices
5.B. Proofs of Some Results
6. Nonlinear Oscillators
6.1. The Rotating Pendulum
6.2. Examples of Eigenvalue Crossings
7. Magnetic Hysteresis
7.1. Curie-Weiss Model
7.2. Ising Model
7.3. Summary and Conclusion
8. Iterated Maps
8.1. Adiabatic Systems
8.2. Slow-Fast Systems
9. Conclusion and Outlook
9.1. Summary of Main Results
9.2. Some Extensions and Open Problems
Bibliography
Index
List of Figures