The non-integrability of the truncated two fixed centres problem (Q1381630)

Recently \textit{M. Irigoyen} [J. Differ. Equ. 131, No. 2, 267-276 (1996; Zbl 0862.58032)] proved that any truncation of order \(\geq 3\) of the symmetric two fixed centers problem is not completely integrable through meromorphic integrals. Using the non-integrability of any truncation of the zonal satellite problem (a recent result of the authors) they point out the fact that neither is any truncation of the asymmetric problem. To this end the authors use results of Ziglin and Yoshida.