Unfoldings of saddle-nodes and their Dulac time

DOI10.1016/j.jde.2016.08.040zbMath1353.34036arXiv1503.04629OpenAlexW1676059085MaRDI QIDQ324121

Mariana Saavedra, Pavao Mardešić, Jordi Villadelprat, David Marin Perez

Publication date: 10 October 2016

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

Full work available at URL: https://arxiv.org/abs/1503.04629

zbMATH Keywords

asymptotic expansionsperiod functionunfolding of a saddle-node

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (8)

Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres ⋮ The criticality of reversible quadratic centers at the outer boundary of its period annulus ⋮ Asymptotic development of an integral operator and boundedness of the criticality of potential centers ⋮ A criticality result for polycycles in a family of quadratic reversible centers ⋮ Analytic tools to bound the criticality at the outer boundary of the period annulus ⋮ Bifurcations of zeros in translated families of functions and applications ⋮ Dulac time of a resonant saddle in the loud family ⋮ Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: local setting

Cites Work

• Briot-Bouquet's theorem in high dimension
• Unfolding of resonant saddles and the Dulac time
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Cyclicité finie des polycycles hyperboliques de champs de vecteurs du plan. Algorithme de finitude. (Finite cyclicity of hyperbolic polycycles of plane vector fields. Finiteness algorithm)
• The period function of reversible quadratic centers
• On the time function of the Dulac map for families of meromorphic vector fields
• Ordinary Differential Equations with Applications
• Reduction of Singularities of the Differential Equation Ady = Bdx
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