Limit cycles, invariant meridians and parallels for polynomial vector fields on the torus

DOI10.1016/j.bulsci.2010.06.005zbMath1221.37034OpenAlexW2051982146MaRDI QIDQ627695

Jaume Llibre, João C. R. Medrado

Publication date: 3 March 2011

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/150441

zbMATH Keywords

limit cycleinvariant toruspolynomial vector fieldinvariant meridianinvariant parallel

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Dynamics induced by flows and semiflows (37C10) Periodic orbits of vector fields and flows (37C27)

Related Items (6)

Polynomial vector fields on algebraic surfaces of revolution ⋮ Invariant parallels, invariant meridians and limit cycles of polynomial vector fields on some 2-dimensional algebraic tori in \(\mathbb R^3\) ⋮ On the number of invariant conics for the polynomial vector fields defined on quadrics ⋮ Invariant hyperplane sections of vector fields on the product of spheres ⋮ When Parallels and Meridians are Limit Cycles for Polynomial Vector Fields on Quadrics of Revolution in the Euclidean 3-Space ⋮ Polynomial Vector Fields on the Clifford Torus

Cites Work

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• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Vector fields, invariant varieties and linear systems.

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