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

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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.

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Correspondence to Valeriia Starichkova.

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Starichkova, V. Global Bifurcations in Generic One-parameter Families on \(\mathbb{S}^2\). Regul. Chaot. Dyn. 23, 767–784 (2018).

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