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Averaging in Difference Equations Driven by Dynamical Systems
 in: Geometric Methods in Dynamics (II), AstÃ©risque 287
, 2003
"... . The averaging setup arises in the study of perturbations of parametric families of dynamical systems when parameters start changing slowly in time. Usually, averaging methods are applied to systems of dierential equations which combine slow and fast motions. This paper deals with dierence equation ..."
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. The averaging setup arises in the study of perturbations of parametric families of dynamical systems when parameters start changing slowly in time. Usually, averaging methods are applied to systems of dierential equations which combine slow and fast motions. This paper deals with dierence equations case which leads to wider class of models and examples. The averaging principle is justied here under a general condition which is veried when unperturbed transformations either preserve smooth measures or they are hyperbolic. The convergence speed in the averaging principle is estimated for some cases, as well. 1.