This article is cited in 7 papers

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

Valeriia Starichkova

Université Paris-Sud 11, Département de Mathématiques, Faculté des Sciences d’Orsay, bâtiment 307, F-91405 Orsay Cedex, France

Abstract: 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.

Keywords: bifurcations, equivalence, structural stability.

MSC: 34C23, 37G99, 37E35

Received: 28.08.2018
Accepted: 23.10.2018

Language: English

DOI: 10.1134/S1560354718060102

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