Limit cycles of the classical Liénard differential systems: a survey on the Lins Neto, de Melo and Pugh's conjecture

DOI10.1016/j.exmath.2016.12.001zbMath1381.34049OpenAlexW2565955656WikidataQ122905759 ScholiaQ122905759MaRDI QIDQ2403622

Xiang Zhang, Jaume Llibre

Publication date: 11 September 2017

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/221320

zbMATH Keywords

Liénard systemlimit cycleconjecture of Lins Neto, de Melo and Pugh

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Averaging method for ordinary differential equations (34C29)

Related Items (3)

Phase portraits of piecewise linear continuous differential systems with two zones separated by a straight line ⋮ Complete bifurcation diagram and global phase portraits of Liénard differential equations of degree four ⋮ Some open problems in low dimensional dynamical systems

Cites Work

• Classical Liénard equations of degree \(n\geqslant 6\) can have \([\frac{n-1}{2}+2\) limit cycles]
• Uniqueness of limit cycles for Liénard differential equations of degree four
• Slow divergence integrals in classical Liénard equations near centers
• Limit cycles for \(m\)-piecewise discontinuous polynomial Liénard differential equations
• Qualitative theory of planar differential systems
• The number of small-amplitude limit cycles of Liénard equations
• More limit cycles than expected in Liénard equations
• Limit cycles of the generalized polynomial Liénard differential equations
• Order of cyclicity of the singular point of lineard's polynomial vector fields
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