Critical periods in planar polynomial centers near a maximum number of cusps

DOI10.1016/j.jde.2023.10.034OpenAlexW4388472244MaRDI QIDQ6140126

Joan Torregrosa, Peter De Maesschalck

Publication date: 19 January 2024

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

Full work available at URL: https://doi.org/10.1016/j.jde.2023.10.034

zbMATH Keywords

Hamiltonian vector fieldscritical periodsbest lower bounddegree \(n\) vector field

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) Periodic orbits of vector fields and flows (37C27) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)

Cites Work

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• The period function of classical Liénard equations
• On the number of critical periods for planar polynomial systems
• On the number of critical periods for planar polynomial systems of arbitrary degree
• On period functions of Liénard systems
• New lower bound for the number of critical periods for planar polynomial systems
• The period function of generalized Loud's centers
• On the critical periods of perturbed isochronous centers
• Cyclicity of a fake saddle inside the quadratic vector fields
• Bifurcation of Critical Periods for Plane Vector Fields
• An Introduction to Catastrophe Theory and Its Applications
• Plane Algebraic Curves with Prescribed Singularities

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