Ergodic Theory and Dynamical Systems

Geometry of KAM tori for nearly integrable Hamiltonian systems

a1 Instituut voor Wiskunde en Informatica, Rijksuniversiteit Groningen, Blauwborgje 3, 9747 AC Groningen, The Netherlands (e-mail:,
a2 Faculteit Wiskunde en Informatica, Universiteit Utrecht, Budapestlaan 6, 3584 CD Utrecht, The Netherlands (e-mail:
a3 Università di Padova, Dipartimento di Matematica Pura e Applicata, Via G. Belzoni 7, 35131 Padova, Italy (e-mail:

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


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)