## Hamiltonian Reduction by StagesIn this volume readers will find for the first time a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. Special emphasis is given to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. Ample background theory on symplectic reduction and cotangent bundle reduction in particular is provided. Novel features of the book are the inclusion of a systematic treatment of the cotangent bundle case, including the identification of cocycles with magnetic terms, as well as the general theory of singular reduction by stages. |

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### Contents

XXXIX | 286 |

XL | 295 |

XLI | 304 |

XLII | 309 |

XLIII | 315 |

XLIV | 321 |

XLV | 347 |

XLVI | 397 |

X | 101 |

XI | 106 |

XII | 110 |

XIII | 113 |

XIV | 119 |

XV | 132 |

XVI | 137 |

XVII | 143 |

XVIII | 144 |

XIX | 149 |

XX | 171 |

XXI | 176 |

XXII | 178 |

XXIII | 198 |

XXIV | 201 |

XXV | 204 |

XXVI | 211 |

XXVII | 212 |

XXVIII | 225 |

XXIX | 239 |

XXX | 240 |

XXXI | 245 |

XXXII | 251 |

XXXIII | 252 |

XXXIV | 253 |

XXXV | 259 |

XXXVI | 267 |

XXXVII | 279 |

XXXVIII | 284 |

### Other editions - View all

Hamiltonian Reduction by Stages Jerrold E. Marsden,Gerard Misiolek,Juan-Pablo Ortega,Matthew Perlmutter,Tudor Ratiu No preview available - 2007 |

Hamiltonian Reduction by Stages Jerrold E. Marsden,Gerard Misiolek,Juan-Pablo Ortega,Matthew Perlmutter,Tudor S. Ratiu No preview available - 2007 |

### Common terms and phrases

Abelian action of G Adº central extension coadjoint action coadjoint orbit cocycle compute connected component cotangent bundle reduction cotangent lift curvature defined denote diffeomorphism dimensional dual element equation equivalent equivariant example formula free and proper function g e G G-action G-invariant given Hamiltonian hence identity induced isomorphism isotropy subgroup Lagrangian left action Lemma Lie algebra Lie group Lie group G Lie-Poisson Marsden mechanical connection momentum map nonequivariant normal subgroup one-cocycle one-form orbit reduction Ortega Poisson bracket Poisson manifold projection Proof Proposition prove quotient Ratiu Recall reduction by stages reduction theorem right translation satisfies semidirect product singular stages hypothesis stages theorem stratification submanifold surjective symplectic diffeomorphism symplectic form symplectic leaves symplectic manifold symplectic reduction symplectic structure symplectomorphic tangent theory Tº G Tºo TºQ two-cocycle two-form vector fields