NON-INTEGRABLE CHARACTER OF HAMILTONIAN SYSTEMS WITH GLOBAL AND SYMMETRIC COUPLING

摘要

A new sufficient condition to prove non-integrability of Hamiltonian systems with symmetric variational equations is proposed. Though the present condition is taken as an extension of Ziglin and Yoshida's ''non-resonant condition'', the algorithmic bottle-neck proving non-integrability in high dimensional cases can be removed here. As a result, the non-existence of additional integrals of various symmetric Hamiltonian systems with an arbitrary number of degrees of freedom is proven. [References: 20]