On algebraic-analytic aspects of the abelian Liouville-Arnold integrability by quadratures of Hamiltonian systems on cotangent spaces

Citation
Ak. Prykarpatsky, On algebraic-analytic aspects of the abelian Liouville-Arnold integrability by quadratures of Hamiltonian systems on cotangent spaces, REP MATH PH, 46(1-2), 2000, pp. 233-243
Citations number
13
Categorie Soggetti
Physics
Journal title
REPORTS ON MATHEMATICAL PHYSICS
ISSN journal
00344877 → ACNP
Volume
46
Issue
1-2
Year of publication
2000
Pages
233 - 243
Database
ISI
SICI code
0034-4877(200008/10)46:1-2<233:OAAOTA>2.0.ZU;2-G
Abstract
A symplectic theory approach is developed for solving the problem of algebr aic-analytical construction of integral submanifold imbedding mapping for i ntegrable via the abelian Liouville-Arnold theorem Hamiltonian systems on c anonically symplectic phase spaces. The related Picard-Fuchs type equations are derived for the first time straightforwardly, making use of a method b ased on generalized Francoise-Galissot-Reeb differential-geometric results. The relationships between toruslike compact integral submanifolds of a Lio uville-Arnold integrable Hamiltonian system and solutions to corresponding Picard-Fuchs type equations is stated.