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Journal Articles Journal of Differential Equations Year : 1993

Perturbed homoclinic solutions in reversible 1:1 resonance vector fields

Abstract

We consider a smooth reversible vector field in R^4, such that the origin is a fixed point. The differential at the origin has two double pure imaginary eigenvalues ±iq for the critical value 0 of the parameter µ. We show, by a normal form analysis, that the vector field can be approximated by an integrable field in R^4, for which we know all solutions. Specially interesting ones are the homoclinics to 0, and homoclinics to periodic solutions, depending on the sign of a leading nonlinear coefficient. We prove in particular the persistence of these homoclinics for the full vector field.
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Dates and versions

hal-01271158 , version 1 (09-02-2016)

Identifiers

  • HAL Id : hal-01271158 , version 1

Cite

Gérard Iooss, Marie-Christine Pérouème. Perturbed homoclinic solutions in reversible 1:1 resonance vector fields. Journal of Differential Equations, 1993, 102 (1), pp.27. ⟨hal-01271158⟩
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