Global bifurcations in generic one-parameter families on \(\mathbb{S}^2\)

DOI10.1134/S1560354718060102zbMath1414.34025OpenAlexW2905257378MaRDI QIDQ1739562

Valeriia V. Starichkova

Publication date: 26 April 2019

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354718060102

zbMATH Keywords

equivalencestructural stabilitybifurcations

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Structural stability and analogous concepts of solutions to ordinary differential equations (34D30) Ordinary differential equations and systems on manifolds (34C40) Equivalence and asymptotic equivalence of ordinary differential equations (34C41)

Related Items (4)

Various equivalence relations in global bifurcation theory ⋮ New structurally unstable families of planar vector fields ⋮ Families of vector fields with many numerical invariants ⋮ First steps of the global bifurcation theory in the plane

Cites Work

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• Hilbert's 16th problem for quadratic vector fields
• Global bifurcations in the two-sphere: a new perspective
• Generic one-parameter families of vector fields on two-dimensional manifolds
• Upper bounds of the number of orbital topological types of polynomial vector fields on the plane “modulo limit cycles”
• Global bifurcations in generic one-parameter families with a parabolic cycle on $S^2$
• Towards the General Theory of Global Planar Bifurcations

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