Journal of Dynamics and Differential Equations

, Volume 6, Issue 1, pp 147-173

First online:

Heteroclinic orbits in singular systems: A unifying approach

  • Flaviano BattelliAffiliated withIstituto di Biomatematica, Universitá

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We consider singularly perturbed systems\(\xi = f(\xi ,\eta ,\varepsilon ),\dot \eta = \varepsilon g(\xi ,\eta ,\varepsilon )\), such thatξ=f(ξ, αo, 0). αo∃ℝ m , 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