Transversal curves for finding the exact number of limit cycles

DOI10.1134/S0012266120040023zbMath1444.34052OpenAlexW3023192461MaRDI QIDQ2185101

Alexander Grin

Publication date: 4 June 2020

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

Full work available at URL: https://doi.org/10.1134/s0012266120040023

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

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Cites Work

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• Upper bounds for the number of limit cycles through linear differential equations
• Dulac-Cherkas test for determining the exact number of limit cycles of autonomous systems on the cylinder
• Dulac-Cherkas criterion for exact estimation of the number of limit cycles of autonomous systems on a plane
• Reduction to transversality of curves in the construction of a Dulac function
• Qualitative theory of planar differential systems
• Dulac-Cherkas functions for generalized Liénard systems
• Centennial History of Hilbert's 16th Problem

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