Reduction to transversality of curves in the construction of a Dulac function

DOI10.1134/S0012266106060139zbMath1154.34321MaRDI QIDQ2459701

Alexander Grin

Publication date: 8 November 2007

Published in: Differential Equations (Search for Journal in Brave)

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items (7)

Dulac-Cherkas criterion for exact estimation of the number of limit cycles of autonomous systems on a plane ⋮ On a Dulac function for the Kukles system ⋮ Transversal curves for finding the exact number of limit cycles ⋮ Limit cycle function of the second kind for autonomous systems on the cylinder ⋮ Estimate of the number of limit cycles of a second-order autonomous system and their localization ⋮ Dulac-Cherkas function in a neighborhood of a structurally unstable focus of an autonomous polynomial system on the plane ⋮ Bendixson-Dulac criterion and reduction to global uniqueness in the problem of estimating the number of limit cycles

Cites Work

• Mathematical problems for the next century
• A precise estimate on the number of limit cycles of autonomous systems on the plane
• An estimate on the number of limit cycles via critical points of conditional extremum
• Extrema of the Andronov-Hopf function of a polynomial Lienard system
• An effective method of counting the number of limit cycles
• Centennial History of Hilbert's 16th Problem
• Algebraic aspects of finding the Dulac function for polynomial autonomous systems in the plane
• A special Dulac function for a quadratic system on the plane
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