On Picard-Fuchs type equations related to integrable Hamiltonian systems

Abstract

The structure properties of integral submanifold imbedding mapping for a class of algebraically Liouville integrable Hamiltonian systems on cotangent phase spaces are studied in relation with Picard -Fuchs type equations. It is shown that these equations can be constructed by making use of a given a priori set of involutive invariants and proved that their solutions in the Hamilton-Jacobi separable variable case give rise to the integral submanifold imbedding mapping, which is known to be a main ingredient for Liouville-Arnold integrability by quadratures of the Hamiltonian system under consideration.