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

Abstract

There are studied in detail the structure properties of integral submanifold imbedding mapping for a class of algebraically Liouville integrable Hamiltonian systems on cotangent phase spaces and related with it so called Picard-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 mapping being as known a main ingredient for Liouville-Arnold integrability by quadratures of the Hamiltonian system under regard. (C) 2001 American Institute of Physics.