On the number of critical periods for planar polynomial systems of arbitrary degree

DOI10.1016/j.jde.2010.01.002zbMath1203.34049OpenAlexW2031615970MaRDI QIDQ984437

Jiazhong Yang, Changjian Liu, Armengol Gasull

Publication date: 19 July 2010

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

Full work available at URL: https://doi.org/10.1016/j.jde.2010.01.002

zbMATH Keywords

Hilbert's 16th problemperiod functioncritical periodreversible center

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) 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) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (14)

Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres ⋮ Existence of kink waves and periodic waves for a perturbed defocusing mKdV equation ⋮ Normal form and limit cycle bifurcation of piecewise smooth differential systems with a center ⋮ Bifurcation of critical periods from the reversible rigidly isochronous centers ⋮ Existence of solitary waves and periodic waves for a perturbed generalized BBM equation ⋮ Critical periods in planar polynomial centers near a maximum number of cusps ⋮ Limit speed of traveling wave solutions for the perturbed generalized KdV equation ⋮ 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 ⋮ Criticality via first order development of the period constants ⋮ The period function and the harmonic balance method ⋮ New lower bounds of the number of critical periods in reversible centers ⋮ Some open problems in low dimensional dynamical systems

Cites Work

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• Polynomial systems: a lower bound for the Hilbert numbers
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