Non-integrability of geodesic flow on certain algebraic surfaces

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 $xyz=1$. 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

References in corpus (2)

• Swinging Atwood's Machine: Experimental and Theoretical Studies
• Regular and irregular geodesics on spherical harmonic surfaces

Cited by in corpus (3)

• Bifurcations of the conjugate locus
• Bi-Hamiltonian Structure of Gradient Systems in Three Dimensions and Geometry of Potential Surfaces
• Integrable geodesic flows on tubular sub-manifolds