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.