This is a modern Hamiltonian theory offering a unified treatment of all types of systems (finite, lattice and field). Particular attention is paid to nonlinear systems that have more than one Hamiltonian formulation in a single co-ordinate system. As this property is closely related to integrability, this book presents an algebraic theory of integrable systems. It is intended for scientists, lecturers and students interested in the field.
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. (Part contents)