ANALYTICAL NONINTEGRABILITY OF THE TRUNCATED 2 FIXED CENTERS PROBLEM IN THE SYMMETRICAL CASE

The Problem of two fixed centres is an integrable Hamiltonian system. If one truncates the Taylor expansion of the potential of this problem (in the symmetric case) at any order greater than or equal to 3, we p rove that one obtains a system which does not admit any first integral , meromorphic and functionally independent of the energy and the angul ar momentum. The proof is mainly founded on the criterion of nonintegr ability for homogeneous potentials, derived by Yoshida from Ziglin's t heorem. Then we use this result to prove that the Vinti Problem, trunc ated at any order greater than or equal to 3, is analytically non-inte grable. (C) 1996 Academic Press, Inc.