Singular points and limit cycles of planar polynomial vector fields

DOI10.1215/S0012-7094-00-10211-6zbMath0953.34021MaRDI QIDQ1975644

I. V. Itenberg, Eugenii I. Shustin

Publication date: 19 July 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

attractorssingular pointslimit cyclessaddlesplanar polynomial systemsrepellers

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Attractors of solutions to ordinary differential equations (34D45)

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Centennial History of Hilbert's 16th Problem, Patchworking singular algebraic curves. I, Patchworking singular algebraic curves. II, Simultaneity of centres in ℤ _q -equivariant systems, The Viro method for construction of Bernstein-Bézier algebraic hypersurface piece, On the number of limit cycles bifurcating from a non-global degenerated center, The 16th Hilbert problem on algebraic limit cycles, On the number of critical periods for planar polynomial systems, On the number of critical periods for planar polynomial systems of arbitrary degree, Minimality and ergodicity of a generic analytic foliation of ℂ², A tropical approach to enumerative geometry, The Viro method for construction of \(C^r\) piecewise algebraic hypersurfaces, Simultaneity of centres in double-reversible planar differential systems, Viro method for the construction of real complete intersections, On the abelian integrals of quadratic reversible centers with orbits formed by genus one curves of higher degree

Cites Work

• The number of roots of a system of equations
• Real plane algebraic curves with prescribed singularities
• Multidimensional generalization of the Il'yashenko theorem on abelian integrals
• Patchworking algebraic curves disproves the Ragsdale conjecture
• Surjectivity of the resultant map: a solution to the inverse bezout problem
• Eleven small limit cycles in a cubic vector field
• Polynomial systems: a lower bound for the Hilbert numbers
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