EXPLICIT DERIVATION OF RETURN MAPS FOR PLANAR VECTOR FIELDS WITH NILPOTENT LINEAR PART WITH A CENTER OR A FOCUS

DOI10.1142/S0219530513500115zbMath1275.34046OpenAlexW1963646817MaRDI QIDQ4923172

Rodica D. Costin

Publication date: 5 June 2013

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

Full work available at URL: https://doi.org/10.1142/s0219530513500115

zbMATH Keywords

first return mapcenter or focusPlanar vector fields with nilpotent linear part

Mathematics Subject Classification ID

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) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Cites Work

• Unnamed Item
• Analytic properties of the return mapping of Liénard equations
• An explicit expression for the first return map in the center problem
• Higher order Poincaré-Pontryagin functions and iterated path integrals
• Iterated integrals, Gelfand-Leray residue, and first return mapping
• The asymptotics to the return map of a singular point with fixed Newton diagram
• The leading term of the first return map of a singular point with a fixed Newton diagram
• Normalizability, synchronicity, and relative exactness for vector fields in \(\mathbb C^2\)
• Generating limit cycles from a nilpotent critical point via normal forms
• Normalizable, integrable and linearizable saddle points in the Lotka-Volterra system
• Hilbert's 16th problem for classical Liénard equations of even degree
• A preparation theorem for codimension-one foliations
• Dulac's memoir “On limit cycles” and related problems of the local theory of differential equations

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