Unicity of KAM tori

• Autores: Henk W. Broer , Floris Takens
• Localización: Ergodic theory and dynamical systems, ISSN 0143-3857, Vol. 27, Nº 3, 2007, págs. 713-724
• Idioma: inglés
• DOI: 10.1017/s0143385706000885
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• Resumen

  • The classical KAM theorem establishes the persistence of invariant Lagrangean tori in nearly integrable Hamiltonian systems. These tori are quasi-periodic with Diophantine frequency vectors and their union is a nowhere dense set of positive measure in phase space. A long-standing question is to what extent the perturbed tori are unique. Using the fact that at the level of tori there exists a Whitney smooth conjugacy between the integrable approximation and its perturbation, we are able to prove this unicity. The unicity result is valid on a closed subset of the Diophantine torus union of full measure.