Ergodic Theory and Dynamical Systems



Geometry of KAM tori for nearly integrable Hamiltonian systems


HENK BROER a1, RICHARD CUSHMAN a2, FRANCESCO FASSÒ a3 and FLORIS TAKENS a1
a1 Instituut voor Wiskunde en Informatica, Rijksuniversiteit Groningen, Blauwborgje 3, 9747 AC Groningen, The Netherlands (e-mail: [email protected], [email protected])
a2 Faculteit Wiskunde en Informatica, Universiteit Utrecht, Budapestlaan 6, 3584 CD Utrecht, The Netherlands (e-mail: [email protected])
a3 Università di Padova, Dipartimento di Matematica Pura e Applicata, Via G. Belzoni 7, 35131 Padova, Italy (e-mail: [email protected])

Article author query
broer h   [Google Scholar] 
cushman r   [Google Scholar] 
fasso f   [Google Scholar] 
takens f   [Google Scholar] 
 

Abstract

We obtain a global version of the Hamiltonian KAM theorem for invariant Lagrangian tori by gluing together local KAM conjugacies with the help of a partition of unity. In this way we find a global Whitney smooth conjugacy between a nearly integrable system and an integrable one. This leads to the preservation of geometry, which allows us to define all non-trivial geometric invariants of an integrable Hamiltonian system (like monodromy) for a nearly integrable one.

(Published Online February 12 2007)
(Received August 1 2005)
(Revised September 12 2006)