Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: local setting

DOI10.1016/J.JDE.2020.06.024zbMath1447.34041OpenAlexW3035834995MaRDI QIDQ778218

David Marin Perez, Jordi Villadelprat

Publication date: 2 July 2020

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2020.06.024

zbMATH Keywords

asymptotic expansionDulac mapDulac timeuniform flatness

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) Bifurcation theory for ordinary differential equations (34C23) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (4)

Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: general setting ⋮ The criticality of reversible quadratic centers at the outer boundary of its period annulus ⋮ Stability and cyclicity of polycycles in non-smooth planar vector fields ⋮ Bifurcations of zeros in translated families of functions and applications

Cites Work

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• Finitely-smooth normal forms of local families of diffeomorphisms and vector fields
• On the time function of the Dulac map for families of meromorphic vector fields
• A Multivariate Faa di Bruno Formula with Applications

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