Conti, Roberto Centers of planar polynomial systems. A review. (English) Zbl 1156.34315 Matematiche 53, No. 2, 207-240 (1998). The author surveys current research on polynomial systems \(dx/dt=\alpha x+\beta y+p(x,y)\), \(dy/dt=\gamma x+\delta y+q(x,y)\) with a center. Three cases are treated separately: (i) total degeneracy, \(\alpha+\beta=\gamma=\delta=0\); (ii) semidegeneracy, \(\alpha\delta-\beta\gamma=0, \alpha+\delta=0, \alpha^2+\beta^2+\gamma^2+\delta^2>0\); (iii) nondegeneracy, \(\alpha\delta-\beta\gamma\not=0\). By means of the coefficients of \(p\) and \(q\), identifications are discussed and integrable systems are considered. Geometrical classifications of centers are discussed in terms of the topology of their neighbourhood. Cited in 26 Documents MSC: 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C25 Periodic solutions to ordinary differential equations 37C27 Periodic orbits of vector fields and flows PDFBibTeX XMLCite \textit{R. Conti}, Matematiche 53, No. 2, 207--240 (1998; Zbl 1156.34315)