Journal of Dynamics and Differential Equations

, Volume 6, Issue 1, pp 147–173

Heteroclinic orbits in singular systems: A unifying approach

  • Flaviano Battelli

DOI: 10.1007/BF02219191

Cite this article as:
Battelli, F. J Dyn Diff Equat (1994) 6: 147. doi:10.1007/BF02219191


We consider singularly perturbed systems\(\xi = f(\xi ,\eta ,\varepsilon ),\dot \eta = \varepsilon g(\xi ,\eta ,\varepsilon )\), such thatξ=f(ξ, αo, 0). αo∃ℝm, has a heteroclinic orbitu(t). We construct a bifurcation functionG(α, ɛ) such that the singular system has a heteroclinic orbit if and only ifG(α, ɛ)=0 has a solutionα=α(ɛ). We also apply this result to recover some theorems that have been proved using different approaches.

Key words

Exponential dichotomiesheteroclinic orbitssingular perturbations

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Flaviano Battelli
    • 1
  1. 1.Istituto di Biomatematica, UniversitáUrbinoItaly