Resolution of the Poincaré problem and nonexistence of algebraic limit cycles in family (I) of Chinese classification

DOI10.1016/j.chaos.2004.06.076zbMath1084.34038OpenAlexW1978556244MaRDI QIDQ1771784

Jordi Sorolla, Isaac A. García, Javier Chavarriga

Publication date: 18 April 2005

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2004.06.076

zbMATH Keywords

Poincaré problemalgebraic limit cycle

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)

Related Items (3)

A survey on the inverse integrating factor ⋮ Classification of Invariant Algebraic Curves and Nonexistence of Algebraic Limit Cycles in Quadratic Systems from Family (I) of the Chinese Classification ⋮ On the Poincaré problem and Liouvillian integrability of quadratic Liénard differential equations

Cites Work

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• The limit cycle of the van der Pol equation is not algebraic
• On the Poincaré problem
• Algebraic limit cycles of degree 4 for quadratic systems
• Necessary conditions for the existence of invariant algebraic curves for planar polynomial systems
• Transcendental limit cycles via the structure of arbitrary degree invariant algebraic curves of polynomial planar vector fields
• Algebraic invariant curves for the Liénard equation
• Reduction of Singularities of the Differential Equation Ady = Bdx

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