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

Citation
Am. Samoilenko et al., On the structure of Picard-Fuchs type equations for Liouville-Arnold integrable Hamiltonian system on cotangent phase spaces, J MATH PHYS, 42(11), 2001, pp. 5358-5370
Citations number
24
Categorie Soggetti
Physics
Journal title
JOURNAL OF MATHEMATICAL PHYSICS
ISSN journal
00222488 → ACNP
Volume
42
Issue
11
Year of publication
2001
Pages
5358 - 5370
Database
ISI
SICI code
0022-2488(200111)42:11<5358:OTSOPT>2.0.ZU;2-T
Abstract
There are studied in detail the structure properties of integral submanifol d imbedding mapping for a class of algebraically Liouville integrable Hamil tonian systems on cotangent phase spaces and related with it so called Pica rd-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 mapp ing being as known a main ingredient for Liouville-Arnold integrability by quadratures of the Hamiltonian system under regard. (C) 2001 American Insti tute of Physics.