Large Deviations and Adiabatic Transitions for Dynamical Systems and Markov Processes in Fully Coupled Averaging
Share this pageYuri Kifer
The work treats dynamical systems given by ordinary differential equations in the form \(\frac{dX^\varepsilon(t)}{dt}=\varepsilon B(X^\varepsilon(t),Y^\varepsilon(t))\) where fast motions \(Y^\varepsilon\) depend on the slow motion \(X^\varepsilon\) (coupled with it) and they are either given by another differential equation \(\frac{dY^\varepsilon(t)}{dt}=b(X^\varepsilon(t), Y^\varepsilon(t))\) or perturbations of an appropriate parametric family of Markov processes with freezed slow variables.
Table of Contents
Table of Contents
Large Deviations and Adiabatic Transitions for Dynamical Systems and Markov Processes in Fully Coupled Averaging
- Contents v6 free
- Preface vii8 free
- Part 1. Hyperbolic Fast Motions 19 free
- 1.1. Introduction 210
- 1.2. Main results 715
- 1.3. Dynamics of Φ[sup(t)][sub(ε)] 1826
- 1.4. Large deviations: preliminaries 2735
- 1.5. Large deviations: Proof of Theorem 1.2.3 3139
- 1.6. Further properties of S-functionals 4048
- 1.7. "Very long" time behavior: exits from a domain 4856
- 1.8. Adiabatic transitions between basins of attractors 5664
- 1.9. Averaging in difference equations 6169
- 1.10. Extensions: stochastic resonance 6573
- 1.11. Young measures approach to averaging 6977
- Part 2. Markov Fast Motions 7583
- 2.1. Introduction 7684
- 2.2. Preliminaries and main results 7785
- 2.3. Large deviations 8795
- 2.4. Verifying assumptions for random evolutions 97105
- 2.5. Further properties of S-functionals 99107
- 2.6. "Very long" time behavior: exits from a domain 103111
- 2.7. Adiabatic transitions between basins of attractors 107115
- 2.8. Averaging in difference equations 111119
- 2.9. Extensions: stochastic resonance 116124
- 2.10. Young measures approach to averaging 119127
- Bibliography 125133
- Index 129137 free