A proof of Kolmogorov's theorem

John Hubbard; Yulij Ilyashenko

doi:10.3934/dcds.2004.10.367

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2004, Volume 10, Issue 1&2: 367-385. Doi: 10.3934/dcds.2004.10.367

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A proof of Kolmogorov's theorem

John Hubbard^1, and
Yulij Ilyashenko¹

1.
Department of Mathematics, Malott Hall, Cornell University, Ithaca, NY 14853

Received: April 30, 2002

Revised: March 31, 2003

Published: December 2003

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Abstract

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.

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Mathematics Subject Classification: Primary: 70H08, 70H07, 70H05.

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