On polynomial integrability of the Euler equations on so(4)

Abstract

El títol de la versió pre-print de l'article és: On the integrability and polynomial integrability of the Euler equations

In this paper we prove that the Euler equations on the Lie algebra so(4) with a diagonal quadratic Hamiltonian either satisfy the Manakov condition, or have at most four functionally independent polynomial first integrals. Also we provide necessary conditions in order that the Euler equations can have a fourth functionally independent polynomial first integral via the Kowalevsky exponents.