Homoclinic period blow-up in reversible and conservative systems
- 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.