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The splitting of separatrices for analytic diffeomorphisms

  • E. Fontich (a1) and C. Simó (a2)
Abstract
Abstract

We study families of diffeomorphisms close to the identity, which tend to it when the parameter goes to zero, and having homoclinic points. We consider the analytical case and we find that the maximum separation between the invariant manifolds, in a given region, is exponentially small with respect to the parameter. The exponent is related to the complex singularities of a flow which is taken as an unperturbed problem. Finally several examples are given.

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[1] M. Braun . On the applicability of the third integral of motion. J. Diff. Eq. 13 (1973), 300318.

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[17] J. Sanders . Melnikov's method and averaging. Cel. Mech. 28 (1982), 171181.

[18] C. Siegel & J. Moser . Lectures on Celestial Mechanics. Springer: Berlin-Heidelberg-NewYork, 1971.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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