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Limit theorems in averaging for dynamical systems

Published online by Cambridge University Press:  14 October 2010

Yuri Kifer
Yuri Kifer
Affiliation:
Institute of Mathematics, Hebrew University, Jerusalem, Givat Ram 91904, Israel
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Abstract

This paper yields diffusion and moderate deviation type asymptotics for solutions of differential equations of the form dZε(t)/dt = εB(Zε(t), fty) where ft is a suspension flow (in particular, a hyperbolic flow) over a sufficiently fast mixing transformation. Such problems emerge in the study of perturbed Hamiltonian systems. These exhibit a new class of limit theorems for dynamical systems and extend a number of previously known results.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 6 , December 1995 , pp. 1143 - 1172
Copyright
Copyright © Cambridge University Press 1995

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