Finite cyclicity of slow-fast Darboux systems with a two-saddle loop

DOI10.1090/proc/12678zbMath1362.34048arXiv1307.4121OpenAlexW2408833036MaRDI QIDQ2817000

Marcin Bobieński, Lyubomir Gavrilov

Publication date: 26 August 2016

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

Full work available at URL: https://arxiv.org/abs/1307.4121

zbMATH Keywords

limit cycleslow-fast systemdouble heteroclinic loop

Mathematics Subject Classification ID

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) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (6)

A survey on the blow-up method for fast-slow systems ⋮ Perturbations of the Hess-Appelrot and the Lagrange cases in the rigid body dynamics ⋮ Bifurcation and number of subharmonic solutions of a 4D non-autonomous slow-fast system and its application ⋮ Unnamed Item ⋮ 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

• Pseudo-abelian integrals: unfolding generic exponential case
• Birth of canard cycles
• Hilbert's 16th problem for quadratic vector fields
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Pseudo-abelian integrals on slow-fast Darboux systems
• On the number of limit cycles which appear by perturbation of Hamiltonian two-saddle cycles of planar vector fields
• Canard cycles and center manifolds
• Abelian integrals and limit cycles
• Multiple canard cycles in generalized Liénard equations

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