Integrable Systems of Classical Mechanics and Lie Algebras Volume I, Volume 1This book offers a systematic presentation of a variety of methods and results concerning integrable systems of classical mechanics. The investigation of integrable systems was an important line of study in the last century, but up until recently only a small number of examples with two or more degrees of freedom were known. In the last fifteen years however, remarkable progress has been made in this field via the so-called isospectral deformation method which makes extensive use of group-theoretical concepts. The book focuses mainly on the development and applications of this new method, and also gives a fairly complete survey of the older classic results. Chapter 1 contains the necessary background material and outlines the isospectral deformation method in a Lie-algebraic form. Chapter 2 gives an account of numerous previously known integrable systems. Chapter 3 deals with many-body systems of generalized Calogero-Moser type, related to root systems of simple Lie algebras. Chapter 4 is devoted to the Toda lattice and its various modifications seen from the group-theoretic point of view. Chapter 5 investigates some additional topics related to many-body systems. The book will be valuable to students as well as researchers. |
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Integrable Systems of Classical Mechanics and Lie Algebras, Volume 1 PERELOMOV No preview available - 2011 |
Common terms and phrases
action of G additional integral algebra g B₁ Calogero F coadjoint orbit compact completely integrable consider coordinates corresponding decomposition defined degrees of freedom denote diagonal differential dimension dynamical system eigenvalues element equations of motion equilibrium configuration equivalent Euclidean geodesic flow given group G Hamiltonian systems Hence Hermitian horospherical integrable systems integrals of motion invariant involution Killing form lattice Lax equation Lax pair Lax representation Let g Lie group Lie-Poisson bracket linear many-body Math moment map momenta noncompact orthogonal oscillator particles phase space Phys Poisson bracket polynomials problem projection quadratic reduced respect root system Section semisimple Lie algebra simple Lie algebra simple roots SL(n solution SU(n subgroup symmetric spaces symplectic manifold systems of type Theorem Toda lattice trajectories variables vector field Weyl group zero ән