A criterion for the non-existence of an additional analytic integral in Hamiltonian systems with n degrees of freedom

Abstract

A sufficient condition for the non-existence of an additional global analytic integral is given for n-degrees of freedom Hamiltonians with a homogeneous potential. The criterion is expressed quite simply in terms of the Kowalevski exponents (KE), which characterize the singularity structure of the solution in the complex t-plane. In particular when n=2, the presence of irrational or imaginary Kowalevski exponents implies the non-existence of an additional analytic integral.