Remark on the number of critical points of the period

DOI10.1006/jdeq.1993.1004zbMath0765.34030OpenAlexW1965536762MaRDI QIDQ1206396

Lyubomir Gavrilov

Publication date: 1 April 1993

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

Full work available at URL: https://doi.org/10.1006/jdeq.1993.1004

zbMATH Keywords

family of periodic solutionssimple critical pointHamiltonian system on the plane

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items (22)

First derivative of the period function with applications ⋮ Periodic waves in the fractional modified Korteweg-de Vries equation ⋮ Periodic Waves of the Modified KdV Equation as Minimizers of a New Variational Problem ⋮ The cyclicity of quadratic reversible systems with a center of genus one and non-Morsean point ⋮ On the Kolmogorov’s condition for a special case of the Kirchhoff top ⋮ A NOTE ON THE CRITICAL PERIODS OF POTENTIAL SYSTEMS ⋮ Reachability of maximal number of critical periods without independence ⋮ The period functions' higher order derivatives ⋮ New lower bound for the number of critical periods for planar polynomial systems ⋮ On the number of critical periods for planar polynomial systems ⋮ The period function for quadratic integrable systems with cubic orbits ⋮ Perturbations from an elliptic Hamiltonian of degree four. II: Cuspidal loop ⋮ Poincaré index and periodic solutions of perturbed autonomous systems ⋮ Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles ⋮ On the period function of reversible quadratic centers with their orbits inside quartics ⋮ Criteria to bound the number of critical periods ⋮ Simultaneous bifurcation of limit cycles and critical periods ⋮ Abelian integrals for cubic vector fields ⋮ Perturbations from a kind of quartic Hamiltonians under general cubic polynomials ⋮ The monotonicity of period function for the codimension four quadratic system \(Q_4\). ⋮ Perturbation from an elliptic Hamiltonian of degree four. III: global centre. ⋮ Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.

This page was built for publication: Remark on the number of critical points of the period