Kifer Yu. Large deviations and adiabatic transitions for dynamical systems and Markov processes in fully coupled averaging. - Providence: American Mathematical Society, 2009. - vii, 129 p.: ill. - (Memoirs of the American Mathematical Society; Vol.201, N 944 (third of 5 numbers )). - Bibliogr.: p.124-127. - Ind.: p.129. - ISBN 978-0-8218-4425-0; ISSN 0065-9266  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Contents

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