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 Störmer 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 <img src="http:/img/fbpe/bjp/v28n4/image197.gif" alt="Image197.gif (1160 bytes)" align="top"> and <img src="http:/img/fbpe/bjp/v28n4/image199.gif" alt="Image199.gif (1022 bytes)" align="top">.
