A proof of Kolmogorov's theorem

Pages: 367 - 385, Volume 10, Issue 1/2, January/February 2004

doi:10.3934/dcds.2004.10.367       Abstract        Full Text (244.6K)       Related Articles

John Hubbard - Department of Mathematics, Malott Hall, Cornell University, Ithaca, NY 14853, United States (email)
Yulij Ilyashenko - Department of Mathematics, Malott Hall, Cornell University, Ithaca, NY 14853, United States (email)

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.

Keywords:  Hamiltonian mechanics, Invariant tori, KAM theory
Mathematics Subject Classification:  Primary: 70H08, 70H07, 70H05.

Received: May 2002;      Revised: April 2003;      Published: October 2003.