Zeitschrift für angewandte Mathematik und Physik ZAMP

, Volume 43, Issue 2, pp 292–318

Homoclinic period blow-up in reversible and conservative systems

  • André Vanderbauwhede
  • Bernold Fiedler
Original Papers

DOI: 10.1007/BF00946632

Cite this article as:
Vanderbauwhede, A. & Fiedler, B. Z. angew. Math. Phys. (1992) 43: 292. doi:10.1007/BF00946632


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.

Copyright information

© Birkhäuser Verlag 1992

Authors and Affiliations

  • André Vanderbauwhede
    • 1
  • Bernold Fiedler
    • 2
  1. 1.Instituut voor Theoretische MechanicaKrijgslaan 281Belgium
  2. 2.Mathematisches Institut AUniversität StuttgartStuttgart 80Germany