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On inclination-flip homoclinic orbit associated to a saddle-node singularity

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Abstract

In this article, we study vector fields bifurcating through a saddlenode equilibrium with an unstable homiclinic orbit. Bifurcating diagrams for two-parameter perturbations of these vector fields are exhibited. It is proved that Smale's horseshoe dynamics, surrounding the bifurcating homoclinic orbit, exists for a large set of such perturbations.

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Authors and Affiliations

  1. Departamento de Métodos Matemáticos, Instituto de Matemática-UFRJ, Rio de Janeiro, RJ, Brasil

    C. A. Morales

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  1. C. A. Morales
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Partially supported by CNPq-Brazil and CONICIT-Venezuela.

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Morales, C.A. On inclination-flip homoclinic orbit associated to a saddle-node singularity. Bol. Soc. Bras. Mat 27, 145–160 (1996). https://doi.org/10.1007/BF01259357

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  • DOI: https://doi.org/10.1007/BF01259357

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