Nonintegrability of the \(ABC\)-flow for \(A=B=C\). (Q1432118)

The author proves that the system \[ \dot x=A\sin z+B\cos y,\quad \dot y=B\sin x+A\cos z,\quad \dot z=C\sin y+B\cos x \] has no real-meromorphic first integral on the torus \(T^3\) in the case \(A^2=B^2=C^2\).