Non-integrability of geodesic flow on certain algebraic surfaces
arXiv:1203.2462 · doi:10.1016/j.physleta.2012.03.016
Abstract
This paper addresses an open problem recently posed by V. Kozlov: a rigorous proof of the non-integrability of the geodesic flow on the cubic surface $x y z=1$. We prove this is the case using the Morales-Ramis theorem and Kovacic algorithm. We also consider some consequences and extensions of this result.
Accepted in Physics Letters A