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2013
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# A. Pronin

119899, Moscow, Vorobyevy gory
M.V.Lomonosov Moscow State University

## Publications:

 Pronin A. V., Treschev D. V. Continuous Averaging in Multi-frequency Slow-fast Systems 2000, vol. 5, no. 2, pp.  157-170 Abstract It is well-known that in real-analytic multi-frequency slow-fast ODE systems the dependence of the right-hand sides on fast angular variables can be reduced to an exponentially small order by a near-identical change of the variables. Realistic constructive estimates for the corresponding exponentially small terms are obtained. Citation: Pronin A. V., Treschev D. V.,  Continuous Averaging in Multi-frequency Slow-fast Systems, Regular and Chaotic Dynamics, 2000, vol. 5, no. 2, pp. 157-170 DOI:10.1070/RD2000v005n02ABEH000138
 Pronin A. V., Treschev D. V. On the Inclusion of Analytic Maps into Analytic Flows 1997, vol. 2, no. 2, pp.  14-24 Abstract We prove a general theorem on the representation of an analytic map isotopic to the identity as the Poincare map in a nonautonomous periodic in time analytic system of ODE. If the map belongs to some Lie group of diffeomorphisms, the vector field determining the ODE can be taken from the corresponding Lie algebra of vector fields. The proof uses a specific averaging procedure. Citation: Pronin A. V., Treschev D. V.,  On the Inclusion of Analytic Maps into Analytic Flows, Regular and Chaotic Dynamics, 1997, vol. 2, no. 2, pp. 14-24 DOI:10.1070/RD1997v002n02ABEH000033