Non-integrability of geodesic flow on certain algebraic surfaces

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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.
Original languageEnglish
JournalPhysics Letters A
Publication statusPublished - 2012


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