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Moscow Mathematical Journal

Volume 14, Issue 4, October–December 2014  pp. 697–709.

A KAM Theorem through Dirichlet's Box and Khintchine's Transference Principles

Authors:  Abed Bounemoura
Author institution:CNRS – CEREMADE, Université Paris Dauphine & IMCCE, Observatoire de Paris


In this paper, we give a new proof of the classical KAM theorem, which avoids small divisors and relies on two basic principles of Diophantine approximation: Dirichlet's box and Khintchine transference principles.

2010 Mathematics Subject Classification. 37J25, 37J40, 70H08, 70H09

Keywords: KAM theory, Diophantine approximation, Khintchine transference

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