Contents
Preface vii
Part 1. Hyperbolic Fast Motions 1
1.1. Introduction 2
1.2. Main results 7
1.3. Dynamics of Φε
t
18
1.4. Large deviations: preliminaries 27
1.5. Large deviations: Proof of Theorem 1.2.3 31
1.6. Further properties of S-functionals 40
1.7. ”Very long” time behavior: exits from a domain 48
1.8. Adiabatic transitions between basins of attractors 56
1.9. Averaging in difference equations 61
1.10. Extensions: stochastic resonance 65
1.11. Young measures approach to averaging 69
Part 2. Markov Fast Motions 75
2.1. Introduction 76
2.2. Preliminaries and main results 77
2.3. Large deviations 87
2.4. Verifying assumptions for random evolutions 97
2.5. Further properties of S-functionals 99
2.6. ”Very long” time behavior: exits from a domain 103
2.7. Adiabatic transitions between basins of attractors 107
2.8. Averaging in difference equations 111
2.9. Extensions: stochastic resonance 116
2.10. Young measures approach to averaging 119
Bibliography 125
Index 129
v
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