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Three dimensional nilpotent singularity and Sil’nikov bifurcation

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  • Li, Xindan
  • Liu, Haifei

Abstract

In this paper, by using the normal form, blow-up theory and the technique of global bifurcations, we study the singularity at the origin with threefold zero eigenvalue for nonsymmetric vector fields with nilpotent linear part and 4-jet C∞-equivalent toy∂∂x+z∂∂y+ax3y∂∂z,with a≠0, and analytically prove the existence of Sil’nikov bifurcation, and then of the strange attractor for certain subfamilies of the nonsymmetric versal unfoldings of this singularity under some conditions.

Suggested Citation

  • Li, Xindan & Liu, Haifei, 2007. "Three dimensional nilpotent singularity and Sil’nikov bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 75-84.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:1:p:75-84
    DOI: 10.1016/j.chaos.2005.09.042
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