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A Global Kam-Theorem: Monodromy in Near-Integrable Pertubrations of Spherical Pendulum

Henk W. Broer,

Data & Software Engineering Research Group
STEI-ITB, Jl. Ganeca No.10, Bandung 40132, Indonesia
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Abstract.

The Kam theory for the persistence of Lagrangean invariant tori in nearly integrable Hamiltonian systems is globalized to bundles of invariant tori. This leads to globally well-defined conjugations between near-integrable systems and their integrable approximations, defined on nowhere dense sets of positive measure associated to Diophantine frequency vectors. These conjugations are Whitney smooth diffeomorphisms between the corresponding torus bundles. Thus the geometry of  the integrable torus bundle is inherited by the near-integrable perturbation. This is of interest in cases where these bundles are non-trivial. The paper deals with the spherical pendulum as a leading example.



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