Regular and Chaotic Dynamics

, Volume 23, Issue 6, pp 767–784 | Cite as

Global Bifurcations in Generic One-parameter Families on \(\mathbb{S}^2\)

  • Valeriia StarichkovaEmail author


In this paper we prove that generic one-parameter families of vector fields on \(\mathbb{S}^2\) in the neighborhood of the fields of classes AH, SN, HC, SC (Andronov–Hopf, saddle-node, homoclinic curve, saddle connection) are structurally stable. We provide a classification of bifurcations in these families.


bifurcations equivalence structural stability 

MSC2010 numbers

34C23 37G99 37E35 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Université Paris-Sud 11, Département de Mathématiques, Faculté des Sciences d’OrsayOrsay CedexFrance

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