## The Problem of Integrable Discretization: Hamiltonian ApproachAn exploration of the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons. Most of the results are only available from recent journal publications, many of them are new. Thus, the book is a kind of encyclopedia on discrete integrable systems. It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems. |

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### Contents

3 | |

10 | |

Rmatrix Hierarchies | 51 |

Lattice Systems | 98 |

Volterra Lattice | 173 |

Newtonian Equations of the Toda Type | 231 |

Relativistic Toda Lattice | 263 |

Relativistic Volterra Lattice | 321 |

Multifield Relativistic Volterra Systems | 567 |

Bogoyavlensky Lattices | 605 |

AblowitzLadik Hierarchy | 643 |

Peakons System | 689 |

Standardlike Discretizations | 701 |

Liealgebraic Toda Systems | 711 |

Garnier System | 777 |

HénonHeiles System | 817 |

Newtonian Equations of the Relativistic Toda Type | 355 |

Explicit Discretizations for Toda Systems | 409 |

BruschiRagnisco Lattice | 445 |

Multifield Todalike Systems | 455 |

Multifield Relativistic Toda Systems | 483 |

BelovChaltikian Lattices | 507 |

Multifield Volterralike Systems | 533 |

Neumann System | 823 |

Liealgebraic Generalizations of the Garnier Systems | 877 |

Integrable Cases of Rigid Body Dynamics | 897 |

Systems of CalogeroMoser Type | 947 |

1001 | |

List of Notations | 1043 |

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The Problem of Integrable Discretization: Hamiltonian Approach Yuri B. Suris No preview available - 2012 |