Parameterization Method for Computing Quasi-periodic Reducible Normally Hyperbolic Invariant Tori

  • Marta Canadell
  • Àlex Haro
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 4)


We consider the problem of numerically computing quasi-periodic normally hyperbolic invariant tori (NHIT) with fixed frequency as well as their invariant bundles. The algorithm is based on a KAM scheme to find the parameterization of a torus with fixed Diophantine frequency (by adjusting parameters of the model), and suitable Floquet transformations that reduce the linearized dynamics to constant coefficients. We apply this method to continue curves of quasi-periodic NHIT of a perturbed dynamical system and to explore the mechanism of breakdown of these invariant tori. We observe in these continuations that the invariant bundles may collide even if the Lyapunov multipliers remain separated.



M.C. and A.H. have been funded by the Spanish grants MTM2009-09723 and MTM2012-32541. M.C. has also been funded by the FPI grant BES-2010-039663 and A.H. by the Catalan grant 2009-SGR-67.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Marta Canadell
    • 1
    • 2
  • Àlex Haro
    • 1
    • 2
  1. 1.Departament de Matemática Aplicada i AnàlisiUniversitat de BarcelonaBarcelonaSpain
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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