2001/05/19 by J. Bruening, Bruening, J., S. Yu. Dobrokhotov +4
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #70K65 #Aquatic and Environmental Studies #Dynamical Systems (math.DS) #FOS: Mathematics #Nuclear physics research studies #Quantum chaos and dynamical systems #math.DS #msc:70K65
paper · pdf · doi:10.48550/arxiv.math/0105164
10 pages, 0 figures
arxiv created 2001/05/19 · openalex publication_date 2001/05/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The problem of averaging for systems with one fast phase was considered from various points of view in many papers. The averaging method of Krylov and Bogolyubov and methods of KAM theory originated this line of research, the most complete results were obtained by Neishtadt, where the coefficients are assumed real analytic. However, in many problems which are interesting from the point of view of applications, analytic dependence ceases to hold in the neighborhoods of some points. We show that one can choose a transformation such that the averaging procedure of Neishtadt is applicable in these neighborhoods and such passage to limit is uniform.