Isochronic centers of a reversible cubic system (Q2761399)

The authors study the reversible cubic system NEWLINE\[NEWLINE\frac{dx}{dt} = -y(1+Dx+Px^2),\quad \frac{dy}{dt} = x - Ax^2-Cy^2-Kx^3-Mxy^2, \tag{1} NEWLINE\]NEWLINE where \(A\), \(C\), \(D\), \(K\), \(M\) and \(P\) are complex constants. They establish 12 classes of systems of type (1) for which a singular point \(O(0,0)\) is an isochronic centre [see \textit{A. P. Vorob'ev}, Dokl. Akad. Nauk BSSR 7, No. 3, 155-156 (1963; Zbl 0126.10403); \textit{K. S. Sibirskij}, Algebraic invariants of differential equations and matrices, Kishinev (1976; Zbl 0334.34014); \textit{V. V. Amel'kin, N. A. Lukashevich} and \textit{A. P. Sadovskij}, Nonlinear oscillations in systems of second order, Minsk (1982; Zbl 0526.70024)].