## Multi-Hamiltonian Theory of Dynamical SystemsA 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. |

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### Contents

Preliminary Considerations | 1 |

Elements of Differential Calculus for Tensor Fields | 13 |

The Theory of Hamiltonian and BiHamiltonian Systems | 41 |

Copyright | |

7 other sections not shown

### Common terms and phrases

according applying appropriate arbitrary bi-Hamiltonian calculations called canonical Casimir commutator compatible condition consider considerations constant constraint construct coordinates corresponding cosymmetries defined Definition denote depend derivative differential direct dynamical system element equal equation equivalent evolution Example exists fact finite dimensional flow formulation functions given gives Hamiltonian Hamiltonian structure Hence hereditary hierarchy identity infinite integrable introduce invariant inverse isospectral Lax equations Lax operators leads Lemma Lie algebra linear manifold master matrix Miura map modified Moreover motion multi-Hamiltonian natural Newton Nijenhuis obtain pair Poisson operator Poisson structure potential powers presented problem Proof quadratic reads recursion operator reduction representation represents respect restricted satisfies separable solutions space spectral stationary flow structure symmetries takes the form tensor tensor field Theorem theory transformation variables vector field