Poincaré map for some polynomial systems of differential equations

DOI10.1070/SM2004v195n07ABEH000832zbMath1077.34032OpenAlexW2058941019MaRDI QIDQ4658319

Victor P. Varin

Publication date: 16 March 2005

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm2004v195n07abeh000832

zbMATH Keywords

bifurcationlimit cyclePoincare mapplanar polynomial systemcentre-focus problem

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items

Center conditions to find certain degenerate centers with characteristic directions, Unnamed Item, Unnamed Item, Center-focus problem for analytic systems with nonzero linear part, Nonlocal singularities on families of periodic solutions to ordinary differential equations, The problem of distinguishing between a centre and a focus in the space of vector fields with given Newton diagram, Center problem for generic degenerate vector fields, Asymptotics of the monodromy transformation in certain classes of monodromy germs, A method for characterizing nilpotent centers, Geometric criterium in the center problem, Approximate calculation of the coefficients of the Dulac series