Algebraic Limit Cycles on Quadratic Polynomial Differential Systems

DOI10.1017/S0013091517000244zbMath1435.34033OpenAlexW2791127808MaRDI QIDQ5228161

Jaume Llibre, Claudia Valls

Publication date: 9 August 2019

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0013091517000244

zbMATH Keywords

algebraic limit cyclequadratic polynomial differential systemquadratic polynomial vector field

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems, Number of limit cycles for planar systems with invariant algebraic curves, A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Invariant algebraic curves and rational first integrals of holomorphic foliations in \(\mathbb C P(2)\)
• On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves
• The 16th Hilbert problem on algebraic limit cycles
• Classification of quadratic systems admitting the existence of an algebraic limit cycle
• Quadratic systems with a unique finite rest point
• On the uniqueness of algebraic limit cycles for quadratic polynomial differential systems with two pairs of equilibrium points at infinity
• Invariant algebraic curves of large degree for quadratic system
• Algebraic limit cycles of degree 4 for quadratic systems
• On the 16th Hilbert problem for algebraic limit cycles
• Invariant algebraic curves and conditions for a centre
• Invariant algebraic curves and rational first integrals for planar polynomial vector fields
• Uniqueness of algebraic limit cycles for quadratic systems