Multi-Hamiltonian Theory of Dynamical Systems

A modern Hamiltonian theory offering a unified treatment of all types of systems (i. e. finite, lattice, and field) is presented. Particular attention is paid to nonlinear systems that have more than one Hamiltonian formulation in a single coordinate system. As this property is closely related to integrability, this book presents an algebraic theory of integrable systems. The book is intended for scientists, lecturers, and students interested in the field. TOC: From the Contents: Preliminary considerations.- Elements of differential calculus for tensor fields.- The theory of Hamiltonian and bi-Hamiltonian systems.- Lax representations of multi-Hamiltonian systems.- Multi-Hamiltonian soliton particles.- Multi-Hamiltonian finite dimensional systems.- Multi-Hamiltonian Lax dynamics.