Conditions for the existence of a center for the Kukles homogeneous systems
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Publication:1609062
DOI10.1016/S0898-1221(02)00098-6zbMath1012.34025MaRDI QIDQ1609062
Publication date: 15 August 2002
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcations of singular points in dynamical systems (37G10)
Related Items (27)
Integrability conditions for complex kukles systems ⋮ On the limit cycles of a class of Kukles type differential systems ⋮ Local cyclicity and criticality in FF-type piecewise smooth cubic and quartic Kukles systems ⋮ Centers and limit cycles of polynomial differential systems of degree \(4\) via averaging theory ⋮ Center, limit cycles and isochronous center of a \(Z_{4}\)-equivariant quintic system ⋮ Integrability Conditions for Complex Homogeneous Kukles Systems ⋮ Limit cycles in Kukles systems of arbitrary degree with invariant ellipse ⋮ A new method to determine isochronous center conditions for polynomial differential systems. ⋮ A complete classification on the center-focus problem of a generalized cubic Kukles system with a nilpotent singular point ⋮ The isochronous center for Kukles homogeneous systems of degree eight ⋮ Maximum number of limit cycles for generalized Kukles differential system ⋮ On the equivalence of singular point quantities and the integrability of a fine critical singular point ⋮ CENTERS FOR THE KUKLES HOMOGENEOUS SYSTEMS WITH EVEN DEGREE ⋮ Center and isochronous center at infinity for differential systems. ⋮ Globally asymptotically stable equilibrium points in Kukles systems ⋮ Implementation of a new algorithm of computation of the Poincaré-Lyapunov constants. ⋮ The isochronous centers for Kukles homogeneous system of degree nine ⋮ Conditions of infinity to be an isochronous centre for a rational differential system ⋮ On a class of polynomial differential systems of degree 4: phase portraits and limit cycles ⋮ Coexistence of limit cycles and invariant algebraic curves for a Kukles system ⋮ A simple method for constructing non-liouvillian first integrals of autonomous planar systems ⋮ Unnamed Item ⋮ The centers and their cyclicity for a class of polynomial differential systems of degree 7 ⋮ LINEAR CENTERS WITH PERTURBATIONS OF DEGREE 2d + 5 ⋮ Centers for the Kukles homogeneous systems with odd degree ⋮ Centers and Limit Cycles of Generalized Kukles Polynomial Differential Systems: Phase Portraits and Limit Cycles ⋮ ON THE LIMIT CYCLES FOR A CLASS OF GENERALIZED KUKLES DIFFERENTIAL SYSTEMS
Cites Work
- Reversible systems
- Computing centre conditions for certain cubic systems
- Isochronicity and commutation of polynomial vector fields
- On the integrability of two-dimensional flows
- Integrability of a linear center perturbed by a fifth degree homogeneous polynomial
- Integrability of a linear center perturbed by a fourth degree homogeneous polynomial
- On the conditions of Kukles for the existence of a Centre
- On the Paper of Jin and Wang Concerning the conditions for a Centre in certain Cubic Systems
- Local Bifurcations of Critical Periods in the Reduced Kukles System
- The centres in the reduced Kukles system
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