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Author:   A.K. Prykarpatsky ,  I.V. Mykytiuk
Publisher:   Springer
Imprint:   Springer
Edition:   1998 ed.
Volume:   443
Dimensions:   Width: 17.00cm , Height: 3.10cm , Length: 24.40cm
Weight:   2.120kg
ISBN:  

9780792350903

ISBN 10:   0792350901
Pages:   559
Publication Date:   30 June 1998
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Dynamical systems with homogeneous configuration spaces.- 1 Dynamical systems with symmetries.- 2 The existence of a maximal involutive set of functions on the orbits of semi-simple elements of a semi-simple Lie algebra.- 3 The integrability criterion and spherical pairs of Lie groups.- 4 Interpolation property of spherical pairs of compact Lie groups.- 5 Spherical pairs of classical simple Lie groups.- 6 Classification of spherical pairs of the exceptional simple Lie algebras.- 7 Classification of spherical pairs of semi-simple Lie groups.- 2 Geometric quantization and integratble dynamical systems.- 1 Connections on line bundles.- 2 Flat partial connections.- 3 Geometric quantization.- 4.1 Introduction.- 5 Examples: geometric quantization of the oscillator type Hamiltonian systems.- 3 Structures on manifolds and algebraic integrability of dynamical systems.- 1 Poisson structures and dynamical systems with symmetries.- 2 The reduction method and Poisson structures on dual spaces of semi-direct sums of Lie algebras.- 3 Nonlinear Neumann type dynamical systems as integrable flows on coadjoint orbits of Lie groups.- 4 Abelian integrals, integrable dynamical systems, and their Lax type representations.- 5 Dual momentum mappings and their applications.- 6 The Lie algebraic setting of Benney-Kaup dynamical systems and associated via Moser Neumann-Bogoliubov oscillatory flows.- 7 The finite-dimensional Moser type of reduction of modified Boussinesq and super-Korteweg-de Vries Hamiltonian systems via the gradient-holonomic algorithm and dual moment maps.- 8 Lax-type of flows on Grassmann manifolds and dual momentum mappings.- 9 On the geometric structure of integrable flows in Grassmann manifolds.- 4 Algebraic methods of quantum statistical mechanics and their applications.-1 Current algebra representation formalism in nonrelativistic quantum mechanics.- 2 Lie current algebra, Hamiltonian operator, and Bogoliubov functional equations.- 3 The secondary quantization method and the spectrum of quantum excitations of a nonlinear Schrödinger type dynamical system.- 4 Unitary representations of the generalized Virasoro algebra.- 5 Algebraic and differential geometric aspects of the integrability of nonlinear dynamical systems on infinite-dimensional functional manifolds.- 1 The current Lie algebra on S1 and its functional representations.- 2 The gradient holonomic algorithm and Lax type representation.- 3 Lagrangian and Hamiltonian formalisms for reduced infinite-dimensional dynamical systems with symmetries.- 4 The algebraic structure of the gradient-holonomic algorithm for Lax type integrable nonlinear dynamical systems.- 5 The integrability of Lie-invariant geometric objects generated by ideals in the Grassmann algebra.- 6 The algebraic structure of the gradient-holonomic algorithm for the Lax-type nonlinear dynamical systems: the reduction via Dirac and the canonical quantization procedure.- 7 Hamiltonian structures of hydrodynamical Benny type dynamical systems and their associated Boltzmann-Vlasov kinetic equations on an axis.- References.

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