Preface ....................................................... vii
Part 1 Hyperbolic Fast Motions ................................. 1
1.1 Introduction ............................................... 2
1.2 Main results ............................................... 7
1.3 Dynamics of Фtε ........................................... 18
1.4 Large deviations: preliminaries ........................... 27
1.5 Large deviations: Proof of Theorem 1.2.3 .................. 31
1.6 Further properties of 5-functional ........................ 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 5-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
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