Desingularization of nilpotent singularities in families of planar vector fields

DOI10.1090/memo/0753zbMath1040.58020OpenAlexW2047659592MaRDI QIDQ4542408

Daniel Panazzolo

Publication date: 4 August 2002

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/memo/0753

zbMATH Keywords

limit cyclesnormal formsdesingularizationfoliationsplanar vector fieldsblowing-upnilpotent singularitiespower geometrylimit periodic setsanalytic unfoldingcanard problemstrict transforms

Mathematics Subject Classification ID

Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Modifications; resolution of singularities (complex-analytic aspects) (32S45) Control problems involving ordinary differential equations (34H05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Singularities of vector fields, topological aspects (58K45)

Related Items (10)

Regular and slow-fast codimension 4 saddle-node bifurcations ⋮ Resolution of singularities of real-analytic vector fields in dimension three ⋮ A survey on the blow-up method for fast-slow systems ⋮ Cyclicity of common slow-fast cycles ⋮ Spectral sequences and parametric normal forms ⋮ Primary birth of canard cycles in slow-fast codimension 3 elliptic bifurcations ⋮ Blowings-Up of Vector Fields ⋮ Singular perturbations and vanishing passage through a turning point ⋮ Quartic Liénard equations with linear damping ⋮ Planar canards with transcritical intersections

This page was built for publication: Desingularization of nilpotent singularities in families of planar vector fields