Geometry of KAM tori for nearly integrable Hamiltonian systems

Details Geometry of KAM tori for nearly integrable Hamiltonian systems Geometry of KAM tori for nearly integrable Hamiltonian systems

2002-10-03

arxiv.org/abs/math/0210043v1

Mathematics

Dynamical Systems

13 pages, 1 figure

Scientific paper

We obtain a global version of the Hamiltonian KAM theorem for invariant Lagrangean tori by glueing together local KAM conjugacies with 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 preservation of geometry, which allows us to define all the nontrivial geometric invariants like monodromy or Chern classes of an integrable system also for near integrable systems.

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