Asymptotic lower bounds on Hilbert numbers using canard cycles

DOI10.1016/j.jde.2019.09.057zbMath1460.34039OpenAlexW2979949698WikidataQ127131382 ScholiaQ127131382MaRDI QIDQ2286682

Peter De Maesschalck, Maria Jesus Alvarez, Rafel Prohens, Bartomeu Coll

Publication date: 22 January 2020

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

Full work available at URL: https://doi.org/10.1016/j.jde.2019.09.057

zbMATH Keywords

limit cycleslow-fast systemcanard cycleHilbert number

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) 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 for ordinary differential equations (34E15) Canard solutions to ordinary differential equations (34E17)

Related Items (6)

Counting configurations of limit cycles and centers ⋮ Cyclicity of periodic annulus and Hopf cyclicity in perturbing a hyper-elliptic Hamiltonian system with a degenerate heteroclinic loop ⋮ Limit cycles for some families of smooth and non-smooth planar systems ⋮ Some open problems in low dimensional dynamical systems ⋮ On the Hilbert number for piecewise linear vector fields with algebraic discontinuity set ⋮ The number of limit cycles for regularized piecewise polynomial systems is unbounded

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