Multi-Hamiltonian Theory of Dynamical Systems

1. Front Matter

   Pages I-X

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2. Preliminary Considerations

   • Maciej Blaszak

   Pages 1-12

3. Elements of Differential Calculus for Tensor Fields

   • Maciej Blaszak

   Pages 13-39

4. The Theory of Hamiltonian and Bi-Hamiltonian Systems

   • Maciej Blaszak

   Pages 41-85

5. Lax Representations of Multi-Hamiltonian Systems

   • Maciej Blaszak

   Pages 87-106

6. Soliton Particles

   • Maciej Blaszak

   Pages 107-134

7. Multi-Hamiltonian Finite Dimensional Systems

   • Maciej Blaszak

   Pages 135-247

8. Multi-Hamiltonian Lax Dynamics in (1+1)-Dimensions

   • Maciej Blaszak

   Pages 249-312

9. Towards a Multi-Hamiltonian Theory of (2+1)-Dimensional Field Systems

   • Maciej Blaszak

   Pages 313-336

10. Back Matter

    Pages 337-350

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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.

• Hamiltonian
• dynamical system
• dynamical systems
• field theory
• invariant
• nonlinear system
• operator algebra
• philosophy of science
• quantum field theory
• tensor
• vector field

• Physics Department, A. Mickiewicz University, Poznań, Poland

  Maciej Błaszak

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