Yuri Kifer 
Large Deviations and Adiabatic Transitions for Dynamical Systems and Markov Processes in Fully Coupled Averaging [PDF ebook] 

The work treats dynamical systems given by ordinary differential equations in the form $/frac{d X^/varepsilon(t)}{dt}=/varepsilon B(X^/varepsilon(t), Y^/varepsilon(t))$ where fast motions $Y^/varepsilon$ depend on the slow motion $X^/varepsilon$ (coupled with it) and they are either given by another differential equation $/frac{d Y^/varepsilon(t)}{dt}=b(X^/varepsilon(t), Y^/varepsilon(t))$ or perturbations of an appropriate parametric family of Markov processes with freezed slow variables.