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. 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. This Ferran Sunyer i Balaguer Prize-winning monograph is the first self-contained and thorough presentation of the theory of Hamiltonian reduction in the presence of singularities. It can serve as a resource for graduate courses and seminars in symplectic and Poisson geometry, mechanics, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.* 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 ...
|Title||:||Momentum Maps and Hamiltonian Reduction|
|Author||:||Juan-Pablo Ortega, Tudor S. Ratiu|
|Publisher||:||Springer Science & Business Media - 2004|