Pseudo-abelian integrals on slow-fast Darboux systems

DOI10.5802/aif.2765zbMath1278.34031arXiv1007.2001OpenAlexW2963260057MaRDI QIDQ2391383

Marcin Bobieński, Pavao Mardešić, Dmitri Novikov

Publication date: 31 July 2013

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.2001

zbMATH Keywords

limit cyclesbifurcationsDarboux integrabilityabelian integralsslow-fast systemspseudo-abelian integrals

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) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (7)

Darboux integrable system with a triple point and pseudo-abelian integrals ⋮ On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields ⋮ Unnamed Item ⋮ Finite cyclicity of slow-fast Darboux systems with a two-saddle loop ⋮ Darboux systems with a cusp point and pseudo-abelian integrals ⋮ The number of limit cycles for regularized piecewise polynomial systems is unbounded ⋮ Cyclicity of canard cycles with hyperbolic saddles located away from the critical curve

Cites Work

• On limit cycles appearing by polynomial perturbation of Darbouxian integrable systems
• Pseudo-abelian integrals: unfolding generic exponential case
• Pseudo-Abelian integrals along Darboux cycles: A codimension one case
• Pseudo-Abelian integrals along Darboux cycles
• Canard cycles and center manifolds
• Abelian integrals and limit cycles
• Multiple canard cycles in generalized Liénard equations

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