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January & February  2004, 10(1&2): 367-385. doi: 10.3934/dcds.2004.10.367

A proof of Kolmogorov's theorem

John Hubbard 1, and  Yulij Ilyashenko 1,

1. 

Department of Mathematics, Malott Hall, Cornell University, Ithaca, NY 14853, United States, United States

Received  May 2002 Revised  April 2003 Published  October 2003

In this paper we will give a proof of Kolmogorov's theorem on the conservation of invariant tori. This proof is close to the one given by Bennettin, Galgani, Giorgilli and Strelcyn in [2]; we follow the outline of their proof, but carry out the steps somewhat differently in several places. In particular, the use of balls rather than polydiscs simplifies several arguments and improves the estimates.
Keywords: Hamiltonian mechanics, Invariant tori, KAM theory.
Mathematics Subject Classification: Primary: 70H08, 70H07, 70H0.
Citation: John Hubbard, Yulij Ilyashenko. A proof of Kolmogorov's theorem. Discrete & Continuous Dynamical Systems, 2004, 10 (1&2) : 367-385. doi: 10.3934/dcds.2004.10.367
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