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In this paper we use the Ziglin-Yoshida method to discuss the determination of non-integrability domains for some classes of homogeneous hamiltonian systems. In particular, we demonstrate the non-integrability of Stormer problem through the reduction of the system to a two-dimensional homogeneous potential. We have also found the non-integrability domains of potentials of the form and .

On the Ziglin-Yoshida analysis for some classes of homogeneous hamiltonian systems