Algebraic invariant curves for the Liénard equation

DOI10.1090/S0002-9947-98-02002-9zbMath0895.34026MaRDI QIDQ4382979

Henryk Żołądek

Publication date: 24 March 1998

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

algebraic limit cyclesalgebraic invariant curves

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (21)

Liouvillian integrability versus Darboux polynomials ⋮ Invariant algebraic curves for Liénard dynamical systems revisited ⋮ The method of Puiseux series and invariant algebraic curves ⋮ Integrability and solvability of polynomial Liénard differential systems ⋮ Classification of Invariant Algebraic Curves and Nonexistence of Algebraic Limit Cycles in Quadratic Systems from Family (I) of the Chinese Classification ⋮ The hyperelliptic limit cycles of the Liénard systems ⋮ Global dynamics of a Wilson polynomial Liénard equation ⋮ Liénard systems for quadratic systems with invariant algebraic curves ⋮ On some open problems in planar differential systems and Hilbert's 16th problem ⋮ Fixed and moving limit cycles for Liénard equations ⋮ Resolution of the Poincaré problem and nonexistence of algebraic limit cycles in family (I) of Chinese classification ⋮ Periodic solutions of second-order differential equations with two-dimensional Lie point symmetry algebra ⋮ Invariant algebraic curves for the cubic Liénard system with linear damping ⋮ Classification of quadratic systems admitting the existence of an algebraic limit cycle ⋮ Invariant algebraic curves and hyperelliptic limit cycles of Liénard systems ⋮ On the Poincaré problem and Liouvillian integrability of quadratic Liénard differential equations ⋮ Phase portraits of the quadratic polynomial Liénard differential systems ⋮ On the number of hyperelliptic limit cycles of Liénard systems ⋮ On the nonexistence of Liouvillian first integrals for generalized Liénard polynomial differential systems ⋮ Transcendental limit cycles via the structure of arbitrary degree invariant algebraic curves of polynomial planar vector fields ⋮ A characterization of the generalized Liénard polynomial differential systems having invariant algebraic curves

Cites Work

• Unnamed Item
• Quadratic systems with center and their perturbations
• The limit cycle of the van der Pol equation is not algebraic
• The classification of reversible cubic systems with center
• Groupes d'automorphismes de $({\bbfC},0)$ et équations différentielles $ydy+\cdots =0$

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