Journal of Dynamics and Differential Equations

, Volume 6, Issue 1, pp 147–173

Heteroclinic orbits in singular systems: A unifying approach

  • Flaviano Battelli
Article

Abstract

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 dichotomies heteroclinic orbits singular perturbations 

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

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

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