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Homoclinic period blow-up in reversible and conservative systems

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Abstract

We show that in conservative systems each non-degenerate homoclinic orbit asymptotic to a hyperbolic equilibrium possesses an associated family of periodic orbits. The family is parametrized by the period, and the periodic orbits accumulate on the homoclinic orbit as the period tends to infinity. A similar result holds for symmetric homoclinic orbits in reversible systems. Our results extend earlier work by Devaney and Henrard, and provide a positive answer to a conjecture of Strömgren. We present a unified approach to both the conservative and the reversible case, based on a technique introduced recently by X.-B. Lin.

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Authors and Affiliations

  1. Instituut voor Theoretische Mechanica, Rijksuniversiteit Gent, B-9000, Krijgslaan 281, Gent, Belgium

    André Vanderbauwhede

  2. Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, D-7000, Stuttgart 80, Germany

    Bernold Fiedler

Authors
  1. André Vanderbauwhede
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  2. Bernold Fiedler
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Dedicated to Prof. Klaus Kirchgässner on the occasion of his sixtieth birthday

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Vanderbauwhede, A., Fiedler, B. Homoclinic period blow-up in reversible and conservative systems. Z. angew. Math. Phys. 43, 292–318 (1992). https://doi.org/10.1007/BF00946632

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  • DOI: https://doi.org/10.1007/BF00946632

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