LDR 03467    a2200349   4500
010    _a9781475738131
       _bbr.
090    _a16471
101    _aeng
102    _aUS
100    _a20180711              frey50       
200    _bM
       _aMomentum Maps and Hamiltonian Reduction
       _fJuan-Pablo Ortega, Tudor S. Ratiu
210    _cBirkhauser
       _aBoston
       _dcop. 2004
215    _a1 vol. (XXXIV-497 p.)
       _cill., portr
       _d24
225    _9169097
       _aProgress in mathematics
       _v222
       _x0743-1643
320    _aBibliogr. p. [443]-476. Index
330    _aPublisher’s description: The use of symmetries and conservation laws in the qualitative description of dynamics has a long history going back to the founders of classical mechanics. In some instances, the symmetries in a dynamical system can be used to simplify its kinematical description via an important procedure that has evolved over the years and is known generically as reduction. The focus of this work is a comprehensive and self-contained presentation of the intimate connection between symmetries, conservation laws, and reduction, treating the singular case in detail. The exposition reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds. This is followed by a discussion of momentum maps and the geometry of conservation laws that are used in the development of symplectic reduction.

Table of contents: Introduction. Manifolds and smooth structures. Lie group actions. Pseudogroups and groupoids. The standard momentum map. Generalizations of the momentum map. Regular symplectic reduction theory. The Symplectic Slice Theorem. Singular reduction and the stratification theorem. Optimal reduction. Poisson reduction. Dual Pairs. Bibliography. Index.

The book 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.
410    _9169095
       _aBirkhäuser
       _tProgress in mathematics
       _x0743-1643
676    _a2010
686    _20
       _9164943
       _a53D20
       _bDifferential geometry -- Symplectic geometry, contact geometry
       _xMomentum maps; symplectic reduction
686    _20
       _9163918
       _a37J05
       _bDynamical systems and ergodic theory -- Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
       _xGeneral theory, relations with symplectic geometry and topology
686    _20
       _9163920
       _a37J15
       _bDynamical systems and ergodic theory -- Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
       _xSymmetries, invariants, invariant manifolds, momentum maps, reduction
686    _20
       _9166006
       _a70G45
       _bMechanics of particles and systems -- General models, approaches, and methods
       _xDifferential-geometric methods
686    _20
       _9166027
       _a70H33
       _bMechanics of particles and systems -- Hamiltonian and Lagrangian mechanics
       _xSymmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction
700    _4070
       _9179926
       _aOrtega
       _bJuan-Pablo
701    _4070
       _9169041
       _aRatiu
       _bTudor Stefan
       _f1950-
856    _uhttp://link.springer.com/book/10.1007/978-1-4757-3811-7
       _zSpringerlink
856    _uhttp://www.ams.org/mathscinet-getitem?mr=2021152
       _zMSN
856    _uhttps://zbmath.org/?q=an:1241.53069
       _zzbMath
905    _aaw
       _b2018
906    _aaw
       _b2018-08-30
001     16471
995    _f12504-01
       _xachat Ebsco
       _918663
       _cCMI
       _20
       _k53 ORT
       _o0
       _eSalle R
       _z72
       _bCMI
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