The center and cyclicity problems for quartic linear-like reversible systems

DOI10.1016/j.na.2019.111593zbMath1446.34046OpenAlexW2967908902WikidataQ127356051 ScholiaQ127356051MaRDI QIDQ2280373

Joan Torregrosa, Leonardo P. C. da Cruz, Valery G. Romanovski

Publication date: 18 December 2019

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://ddd.uab.cat/record/221386

zbMATH Keywords

center-focus problemcenter cyclicitylinear-like reversible centersquartic centers

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) Symmetries, invariants of ordinary differential equations (34C14) 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)

Related Items

Symmetric centers on planar cubic differential systems ⋮ On the Gröbner basis of the ideal of Lyapunov quantities of the Kukles system

Uses Software

• SINGULAR
• primdec

Cites Work

• Solution of center-focus problem for a class of cubic systems
• Bifurcation of limit cycles from quadratic isochrones
• Integrability of complex planar systems with homogeneous nonlinearities
• Gröbner bases and primary decomposition of polynomial ideals
• Quadratic systems with center and their perturbations
• Quadratic-like cubic systems
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Solution of the center-focus problem for a cubic system reducible to a Liénard system
• Qualitative theory of planar differential systems
• The Center and Cyclicity Problems
• Bifurcation of Critical Periods for Plane Vector Fields
• P-adic reconstruction of rational numbers
• New lower bounds for the Hilbert numbers using reversible centers
• Probleme General de la Stabilite du Mouvement. (AM-17)
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