This paper addresses an open problem recently posed by V. Kovloz in this journal: a rigorous proof of the non-integrability of the geodesic flow on the cubic surface $x y z=1$. We prove this result using the Morales-Ramis theorem and Kovacic algorithm. We also consider some consequences and extensions of this result.
|Journal||Physics Letters A|
|Publication status||Published - 2012|