On general algebraic mechanisms for producing centers in polynomial differential systems

DOI10.1007/s11784-008-0077-2zbMath1162.34022OpenAlexW2007708146MaRDI QIDQ948488

Colin Christopher, Dana Schlomiuk

Publication date: 16 October 2008

Published in: Journal of Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11784-008-0077-2

zbMATH Keywords

symmetrycenterLiouvillian first integralDarboux first integralalgebraic transformationgeneralized polynomial Liénard systems

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

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Homogeneous-like generalized cubic systems ⋮ Small-amplitude limit cycles of certain planar differential systems ⋮ Liénard Equation and Its Generalizations ⋮ Weierstrass integrability in Liénard differential systems ⋮ The application of Liénard transformations to predator-prey systems ⋮ TWO GENERAL CENTRE PRODUCING SYSTEMS FOR THE POINCARÉ PROBLEM ⋮ Center conditions for polynomial Liénard systems ⋮ Solution of the center-focus problem for a nine-parameter cubic system ⋮ Quadratic double centers and their perturbations ⋮ Algebraic approach to the classification of centers in trigonometric Cherkas systems ⋮ Center conditions for generalized polynomial Kukles systems ⋮ Center problem for trigonometric Liénard systems ⋮ Orbitally symmetric systems with applications to planar centers ⋮ Simultaneous integrability and non-linearizability at arbitrary double weak saddles and sole weak focus of a cubic Liénard system ⋮ The CD45 Case Revisited ⋮ Nondegenerate centers for Abel polynomial differential equations of second kind

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