Journal of Dynamics and Differential Equations

, Volume 24, Issue 4, pp 685–711 | Cite as

Tracing KAM Tori in Presymplectic Dynamical Systems

  • Hassan Najafi AlishahEmail author
  • Rafael de la Llave


We present a KAM theorem for presymplectic dynamical systems. The theorem has a “a posteriori” format. We show that given a Diophantine frequency ω and a family of presymplectic mappings, if we find an embedded torus which is approximately invariant with rotation ω such that the torus and the family of mappings satisfy some explicit non-degeneracy condition, then we can find an embedded torus and a value of the parameter close to the original one so that the torus is invariant under the map associated to the value of the parameter. Furthermore, we show that the dimension of the parameter space is reduced if we assume that the systems are exact.


KAM theory Presymplectic structure Quasi-periodic motions Invariant tori 

Mathematics Subject Classification (2000)

70K43 70K20 34D35 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsInstituto Superior TecnicoLisbonPortugal
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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