Non-integrability of geodesic flow on certain algebraic surfaces

Details Non-integrability of geodesic flow on certain algebraic surfaces Non-integrability of geodesic flow on certain algebraic surfaces

2012-03-12

arxiv.org/abs/1203.2462v1

Mathematics

Dynamical Systems

Accepted in Physics Letters A

Scientific paper

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.

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