Averaging under Fast Quasiperiodic Forcing

  • Carles Simó
Part of the NATO ASI Series book series (NSSB, volume 331)

Abstract

We consider a non autonomous system of ordinary differential equations. Assume that the time dependence is quasiperiodic with large basic frequencies, ω/ε and that the ω vector satisfies a diophantine condition. Under suitable hypothesis of analyticity, there exists an analytic (time depending) change of coordinates, such that the new vector field is the sum of an autonomous part and a time dependent remainder. The remainder has an exponentially small bound of the form exp(− a ), where c and a are positive constants. The proof is obtained by iteration of an averaging process. An application is made to the splitting of the separatrices of a two-dimensional normally hyperbolic torus, including several aspects: formal approximation of the torus and their invariant manifolds, numerical computations of the splitting, a first order analysis using a Melnikov approach and the bifurcations of the set of homoclinic orbits.

Keywords

Invariant Manifold Homoclinic Orbit Invariant Torus Moderate Time Interval Melnikov Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Carles Simó
    • 1
  1. 1.Departament de Matemàtica Aplicada i AnàlisiUniversitat de BarcelonaBarcelonaSpain

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