Bakhtin, V. I. On the averaging method in a system with fast hyperbolic motions. (Russian. English summary) Zbl 0954.37017 Tr. Inst. Mat., Minsk 6, 23-26 (2000). The averaging principle for the dynamical systems with fast and slow motions is studied. It is supposed that the fast motions depend on the slow one and goes along a hyperbolic intermixing attractor. A smooth averaged system is constructed. A variant of the central limit theorem is proved, i.e. the Cramer asymptotic for the slow variable large deviations is found. Reviewer: Sergei V.Rogosin (Minsk) Cited in 1 Document MSC: 37D05 Dynamical systems with hyperbolic orbits and sets 37H05 General theory of random and stochastic dynamical systems 37C70 Attractors and repellers of smooth dynamical systems and their topological structure Keywords:dynamical systems; averaging method; fast and slow motion; large deviation; Cramer’s asymptotic PDFBibTeX XMLCite \textit{V. I. Bakhtin}, Tr. Inst. Mat., Minsk 6, 23--26 (2000; Zbl 0954.37017)