On the number of critical points of the period

DOI10.1016/0022-0396(86)90071-9zbMath0594.34028OpenAlexW2088967503MaRDI QIDQ1076876

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1016/0022-0396(86)90071-9

zbMATH Keywords

steady-state solutions bifurcation theory Picard-Fuchs equation cubic polynomial second order differential equation

Mathematics Subject Classification ID

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

Related Items

Existence of kink waves and periodic waves for a perturbed defocusing mKdV equation, Finiteness for critical periods of planar analytic vector fields, Periodic waves in the fractional modified Korteweg-de Vries equation, The monotonicity of the period function for planar Hamiltonian vector fields, The period function of potential systems of polynomials with real zeros, A Higher-Order Period Function and Its Application, Periodic Waves of the Modified KdV Equation as Minimizers of a New Variational Problem, Monotonicity of the period function of the Liénard equation of second kind, The cyclicity of quadratic reversible systems with a center of genus one and non-Morsean point, Existence of solitary waves and periodic waves for a perturbed generalized BBM equation, Perturbed rigidly isochronous centers and their critical periods, Periodic solutions of a second-order differential equation with one-sided growth restrictions on the restoring term, On the isoenergetical non-degeneracy of the problem of two centres of gravitation, On the Kolmogorov’s condition for a special case of the Kirchhoff top, A NOTE ON THE CRITICAL PERIODS OF POTENTIAL SYSTEMS, Limit speed of traveling wave solutions for the perturbed generalized KdV equation, Reachability of maximal number of critical periods without independence, The critical points of the period function of x″−x2(x−α)(x−1)=0 (0⩽α<1), The period functions' higher order derivatives, New lower bound for the number of critical periods for planar polynomial systems, Oscillations and stability in quasiautonomous system. II. Critical point of the one-parameter family of periodic motions, Quasiautonomous system: oscillations, stability, and stabilization at the ordinary point of the family of periodic solutions, A note on the instability of spatially quasi-periodic states of the Ginzburg-Landau equation, Critical periods of perturbations of reversible rigidly isochronous centers, Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators, Monotonicity of limit wave speed of traveling wave solutions for a perturbed generalized KdV equation, Critical periods of perturbations of reversible rigidly isochronous centers, Properties of the period function for some Hamiltonian systems and homogeneous solutions of a semilinear elliptic equation, Solitary waves and periodic waves in a perturbed KdV equation, The monotonicity and critical periods of periodic waves of the \(\varphi^{6}\) field model, The period function for quadratic integrable systems with cubic orbits, On the period function for a family of complex differential equations, Perturbations from an elliptic Hamiltonian of degree four. II: Cuspidal loop, Poincaré index and periodic solutions of perturbed autonomous systems, Geometric methods for two-point nonlinear boundary value problems, Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles, Dynamics of traveling waves for the perturbed generalized KdV equation, On the period function of reversible quadratic centers with their orbits inside quartics, Criteria to bound the number of critical periods, A normally elliptic Hamiltonian bifurcation, The quasi-periodic centre-saddle bifurcation, Simultaneous bifurcation of limit cycles and critical periods, A Quadratic System with a Nonmonotonic Period Function, Abelian integrals for cubic vector fields, Bifurcation of Critical Periods for Plane Vector Fields, The monotonicity of period function for the codimension four quadratic system \(Q_4\)., Bifurcation of limit cycles from quadratic isochrones, Unnamed Item, Bifurcation of critical periods of polynomial systems, Perturbation from an elliptic Hamiltonian of degree four. III: global centre.

Cites Work