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Jordan obstruction to the integrability of Hamiltonian systems with homogeneous potentials

Guillaume Duval, Andrzej J. Maciejewski (2009)

Annales de l’institut Fourier

In this paper, we consider the natural complex Hamiltonian systems with homogeneous potential V ( q ) , q n , of degree k . The known results of Morales and Ramis give necessary conditions for the complete integrability of such systems. These conditions are expressed in terms of the eigenvalues of the Hessian matrix V ( c ) calculated at a non-zero point c n , such that V ( c ) = c . The main aim of this paper is to show that there are other obstructions for the integrability which appear if the matrix V ( c ) is not diagonalizable....

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