On the structure of Picard-Fuchs type equations for Liouville-Arnold integrable Hamiltonian system on cotangent phase spaces

There are studied in detail the structure properties of integral submanifol d imbedding mapping for a class of algebraically Liouville integrable Hamil tonian systems on cotangent phase spaces and related with it so called Pica rd-Fuchs type equations. It is shown that these equations can be in general regularly constructed making use of a given a priori system of involutive invariants and proved that their solutions in the Hamolton-Jacobi separable variable case give rise exactly to the integral submanifold imbedding mapp ing being as known a main ingredient for Liouville-Arnold integrability by quadratures of the Hamiltonian system under regard. (C) 2001 American Insti tute of Physics.