Classification of quadratic systems admitting the existence of an algebraic limit cycle

DOI10.1016/j.bulsci.2006.03.014zbMath1132.34028OpenAlexW2207396809MaRDI QIDQ996969

Grzegorz Świrszcz, Jaume Llibre

Publication date: 19 July 2007

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2006.03.014

zbMATH Keywords

invariant algebraic curvequadratic systemalgebraic limit cycles

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Dynamics induced by flows and semiflows (37C10)

Related Items (14)

Algebraic limit cycles for quadratic polynomial differential systems ⋮ Characterization and bifurcation diagram of the family of quadratic differential systems with an invariant ellipse in terms of invariant polynomials ⋮ On the birth and death of algebraic limit cycles in quadratic differential systems ⋮ Relationships between limit cycles and algebraic invariant curves for quadratic systems ⋮ Algebraic Limit Cycles Bifurcating from Algebraic Ovals of Quadratic Centers ⋮ Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ On the uniqueness of algebraic limit cycles for quadratic polynomial differential systems with two pairs of equilibrium points at infinity ⋮ The hyperelliptic limit cycles of the Liénard systems ⋮ Number of limit cycles for planar systems with invariant algebraic curves ⋮ On the limit cycles bifurcating from an ellipse of a quadratic center ⋮ Algebraic Limit Cycles in Piecewise Linear Differential Systems ⋮ The cubic polynomial differential systems with two circles as algebraic limit cycles ⋮ A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems ⋮ Algebraic Limit Cycles on Quadratic Polynomial Differential Systems

Cites Work

• Relationships between limit cycles and algebraic invariant curves for quadratic systems
• Invariant algebraic curves of large degree for quadratic system
• Algebraic limit cycles of degree 4 for quadratic systems
• Necessary conditions for the existence of invariant algebraic curves for planar polynomial systems
• A survey of quadratic systems
• On the nonexistence, existence and uniqueness of limit cycles
• Algebraic invariant curves for the Liénard equation
• The Geometry of Quadratic Differential Systems with a Weak Focus of Third Order
• On a Result of Darboux
• AN ALGORITHM FOR FINDING INVARIANT ALGEBRAIC CURVES OF A GIVEN DEGREE FOR POLYNOMIAL PLANAR VECTOR FIELDS
• Uniqueness of algebraic limit cycles for quadratic systems
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