quartonews.it » Math and Science » Momentum Maps and Hamiltonian Reduction

Author: | Tudor S. Ratiu,Juan-Pablo Ortega |

Subcategory: | Mathematics |

Language: | English |

Publisher: | Birkhäuser; 2004 edition (December 16, 2003) |

Pages: | 320 pages |

Category: | Math and Science |

Rating: | 4.1 |

Other formats: | doc azw docx mobi |

Juan-Pablo Ortega, Tudor S. Ratiu.

Juan-Pablo Ortega, Tudor S. The use of the symmetries of a physical system in the study of its dynamics has a long history that goes back to the founders of c1assical mechanics. Symmetry-based tech niques are often implemented by using the integrals 01 motion that one can sometimes associate to these symmetries. The integrals of motion of a dynamical system are quan tities that are conserved along the fiow of that system.

Authors: Ortega, Juan-Pablo, Ratiu, Tudor. This is followed by a discussion of momentum maps and the geometry of conservation laws that are used in the development of symplectic reduction. The Symplectic Slice Theorem, an important tool that gave rise to the first description of symplectic singular reduced spaces, is also treated in detail, as well as the Reconstruction Equations that have been crucial in applications to the study of symmetric mechanical systems.

заметки, скачав книгу "Momentum Maps and Hamiltonian Reduction" для чтения в офлайн-режиме. For the his tory of the momentum map we refer to WEINSTEIN (1983b) and MARSDEN AND RATIU (1999), §11. 2. Подробне. крыть.

Выделяйте текст, добавляйте закладки и делайте заметки, скачав книгу "Momentum Maps and Hamiltonian Reduction" для чтения в офлайн-режиме. Правила публикации отзывов.

University of S. allen. The classical phase space is given by the associated Hamiltonian G-manifold and the reduced classical phase space is obtained from that by symplectic reduction. We do not need the details here.

The present book offers a thorough description of theory and a unified treatment of most of its developments and generalizations, with a particular emphasis on those due to the authors. It contains many important results which cannot be found in other books, and covers a large part of the recent developments related to momentum maps and reduction. It's easy to get started - we will give you example code.

Regular symplectic reduction theory. The Symplectic Slice Theorem. oceedings{, title {Momentum Maps and Hamiltonian Reduction}, author {Juan-Pablo Ortega and Tudor S. Ratiu}, year {2003} }. Juan-Pablo Ortega, Tudor S. Singular reduction and the stratification theorem.

Symmetries of Hamiltonian Dynamical Systems, Momentum Maps and Reductions Marle, Charles-Michel,, 2014. Reduction and duality in generalize geometry Hu, Shengda, Journal of Symplectic Geometry, 2007. Momentum Maps and Morita Equivalence Xu, Ping, Journal of Differential Geometry, 2004. Smooth and Peaked Solitons of the Camassa-Holm Equation and Applications Holm, Darryl and Ivanov, Rossen, Journal of Geometry and Symmetry in Physics, 2011. Manin Pairs and Moment Maps Alekseev, Anton and Kosmann-Schwarzbach, Yvette, Journal of Differential Geometry, 2000.

Описание: This book explores the foundations of hamiltonian dynamical systems and statistical mechanics, in. .The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping.

Описание: This book explores the foundations of hamiltonian dynamical systems and statistical mechanics, in particular phase transitionsc, from the point of view of geometry and topology.

Momentum maps and Hamiltonian reduction. Reduction of Poisson manifolds. Letters in Mathematical Physics 11 (2), 161-169, 1986. Progress in Mathematics, Birkhäuser Boston, 2003. Introduction to mechanics and symmetry. JE Marsden, TS Ratiu. Physics Today 48 (12), 65, 1995. Euler-Poincaré models of ideal fluids with nonlinear dispersion. DD Holm, JE Marsden, TS Ratiu.

* Winner of the Ferran Sunyer i Balaguer Prize in 2000.

* Reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds.* Currently in classroom use in Europe.

* Can serve as a resource for graduate courses and seminars in Hamiltonian mechanics and symmetry, symplectic and Poisson geometry, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.

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