My Library: Completely integrable and superintegrable Hamiltonian systems with noncompact invariant submanifolds

The file Library6.pdf (3Mb) contains the attached PDF files of my main works on generalization of Noether theorems to an arbitrary Lagrangian system  Generalization of the Liouville - Arnold, Nekhoroshev and Mishchenko - Fomenko theorems on action-angle variables of completely integrable, partially integrable and superintegrable Hamiltonian systems to the case of non-compact invariant submanifolds.

Contents

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Action-angle coordinates for time-dependent completely integrable Hamiltonian systems, J. Phys. A 35 (2002) L439-L445

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Geometric quantization of completely integrable Hamiltonian systems in action-angle coordinates, Phys. Lett. A 301 (2002) 53-57

E.Fiorani, G.Giachetta and G.Sardanashvily, Geometric quantization of time-dependent completely integrable Hamiltonian systems, J. Math. Phys. 43 (2002) 5013-5025

E.Fiorani, G.Giachetta and G.Sardanashvily, The Liouville -- Arnold -- Nekhoroshev theorem for non-compact invariant manifolds, J. Phys. A 36 (2003) L101-L107

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Jacobi fields of completely integrable systems, Phys. Lett. A 309 (2003) 382-386

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Bi-Hamiltonian partially integrable systems, J. Math. Phys. 44 (2003) 1984-1987

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Nonadiabatic holonomy operators in classical and quantum completely integrable systems, J. Math. Phys. 45 (2004) 76-86

E.Fiorani and G.Sardanashvily, Noncommutative integrability on noncompact invariant manifolds, J. Phys. A 39 (2006) 14035-14042

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Quantization of noncommutative completely integrable systems, Phys. Lett. A 362 (2007) 138-142

E.Fiorani and G.Sardanashvily, Global action-angle coordinates for completely integrable systems with noncompact invariant submanifolds, J. Math. Phys. 48 (2007) 032901

G.Sardanashvily, Superintegrable Hamiltonian systems with noncompact invariant submanifolds. Kepler system, Int. J. Geom. Methods Mod. Phys. 6 (2009) 1391-1420

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Geometric Formulation of Classical and Quantum Mechanics (World Scientific, Singapore, 2010)