Complex integrability and linearizability of cubic \(Z_2\)-equivariant systems with two \(1:q\) resonant singular points (Q1981755)

This paper is concerned with complex integrability and linearizability of cubic \(\mathrm{Z}_2\)-equivariant systems with two \(1:q\) resonant singular points, which generalizes results in the reference [\textit{F. Li} et al., J. Differ. Equations 269, No. 10, 9026--9049 (2020; Zbl 1450.37052)]. The authors overcame the difficulty of computing the saddle values and periodic constants associated with \(1:q\) resonant saddle points and obtain conditions on integrability and linearizability based on computing saddle quantities and periodic constants, respectively.