Limit cycles of polynomial systems with homogeneous non-linearities

DOI10.1016/0022-247X(89)90021-8zbMath0678.34029MaRDI QIDQ1124026

Jaume Llibre, Marc Carbonell

Publication date: 1989

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

limit cyclesvector fieldstwo-dimensional autonomous systemsnon-degenerate critical point

Mathematics Subject Classification ID

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

Related Items

On the limit cycles of polynomial differential systems with homogeneous nonlinearities, On the Limit Cycles of the Polynomial Differential Systems with a Linear Node and Homogeneous Nonlinearities, Centers and limit cycles for a family of Abel equations, Global planar dynamics with a star node and contracting nonlinearity, Global analyses of a class of cubic systems, Unnamed Item, HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS, Limit cycles for cubic systems with a symmetry of order 4 and without infinite critical points, On the limit cycles surrounding a diagonalizable linear node with homogeneous nonlinearities, Bifurcation of limit cycles from a 4-dimensional center in \(\mathbb R^m\) in resonance \(1:N\), Cyclicity of a critical point and the inverse Poincaré map, On the uniqueness and expression of limit cycles in planar polynomial differential system via monotone iterative technique, Limit cycles for 3-monomial differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Further considerations on the number of limit cycles of vector fields of the form \(X(v)=Av+f(v)Bv\)
• A simple class of quadratic systems
• Limit cycles of vector fields of the form \(X(v)=Av+f(v)Bv\)
• Limit cycles of a class of polynomial vector fields in the plane
• On the number of solutions of the equation \(\sum^n_{j=0}a_j(t)x^j,0\leq t\leq 1\), for which \(x(0)=x(1)\)
• Limit cycles of planar quadratic differential equations
• Rotated vector fields and the global behavior of limit cycles for a class of quadratic systems in the plane
• Some theorems on the existence, uniqueness, and nonexistence of limit cycles for quadratic systems
• Limit-cycles and rotated vector fields
• Limit cycles of a class of polynomial systems
• The stability of second-order quadratic differential equations
• A Note on the Number of Limit Cycles in Certain Two-Dimensional Systems
• Non-autonomous equations related to polynomial two-dimensional systems
• The Number of Periodic Solutions of the Equation Ż=z ^N +p ₁ (t )z ^{N −1} +…+p _N (t )
• Generic Properties of Polynomial Vector Fields at Infinity