Invariant algebraic curves and hyperelliptic limit cycles of Liénard systems

DOI10.1007/s12346-021-00484-8zbMath1478.34041OpenAlexW3158862444MaRDI QIDQ2037344

Xinjie Qian, Jiazhong Yang, Yang Shen

Publication date: 30 June 2021

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-021-00484-8

zbMATH Keywords

Liénard systems16th Hilbert probleminvariant algebraic curveshyperelliptic limit cycles

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) Invariant manifolds for ordinary differential equations (34C45)

Related Items (1)

A characterization of the generalized Liénard polynomial differential systems having invariant algebraic curves

Cites Work

• The hyperelliptic limit cycles of the Liénard systems
• The limit cycle of the van der Pol equation is not algebraic
• On the number of hyperelliptic limit cycles of Liénard systems
• Invariant algebraic curves for the cubic Liénard system with linear damping
• On the hyperelliptic limit cycles of Liénard systems
• On the algebraic limit cycles of Liénard systems
• Algebraic invariant curves for the Liénard equation
• Centennial History of Hilbert's 16th Problem
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS

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