ON ALGEBRAIC-ANALYTIC ASPECTS OF THE ABELIAN LIOUVILLE-ARNOLD INTEGRABILITY BY QUADRATURES OF HAMILTONIAN SYSTEMS ON COTANGENT SPACES

A symplectic theory approach is developed for solving the problem of Aalgebraic-analytical construction of integral submanifold imbedding Amapping for integrable via the abelian Liouville-Arnold theorem AHamiltonian systems on canonically symplec-tic phase spaces. The Arelated Picard-Fuchs type equations are derived for the first time straightforwardly, making use of a method based on generalized AFrancoise-Galissot-Reeb differential-geometric results. The Arelationships between toruslike compact integral submanifolds of a ALiouville-Arnold integrable Hamiltonian system and solutions to Acorresponding Picard-Fuchs type equations is stated.