Momentum Maps and Hamiltonian Reduction

By Juan-Pablo Ortega, Tudor S. Ratiu. 2003

471 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2f16051ca759620187c2cda01688d4cdfa2feed6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Control and Systems Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

The holonomy groupoid of a singular foliation (2006, unknown): “the monograph [21]).”
Calabi flow, Geodesic rays, and uniqueness of constant scalar curvature K\ (2010, background): “(Marle-Guillemin-Sternberg [GS], [OR]) There exists a symplectic form ω defined in a neighborhood U of [e, 0, 0] in Y , under which the G action is Hamiltonian with a moment map given by μ : U → g; [g, ρ, v] → Adg(μN (v) + ρ).”
REDUCTION, RECONSTRUCTION, AND SKEW-PRODUCT DECOMPOSITION OF SYMMETRIC STOCHASTIC DIFFERENTIAL EQUATIONS (2007, background): “We recall (see [ OR04 ] for a proof) that for any g ∈ G, ξ ∈ g, and z ∈ M,”
The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits (2006, background): “On the other hand, the notion of a Banach Lie–Poisson space was recently introduced in [28] and is an infinitedimensional version of the Lie–Poisson spaces, that is, the Poisson manifolds provided by dual spaces of finite-dimensional Lie algebras (see for instance [31] for the finite-dimensional the”
Singular reduction of implicit Hamiltonian systems (2003, background): “The results extend the singular reduction theory known for explicit symplectic or Poisson Hamiltonian systems [3, 4, 9, 10, 11, 23, 24, 27].”
Symplectic theory of completely integrable Hamiltonian systems (2011, unknown): “Convexity in the case of Poisson actions has been studied by Alekseev [3], Flaschka and Ratiu [45], Ortega and Ratiu [82], and Weinstein [119] among others.”
Hamiltonian Symmetries and Reduction in Generalized Geometry (2005, background): “the relation with variational principles, see for example [42, 43]. The reduction in singular cases for the Poisson and Dirac structures are also known, e.g. [50], [11], as well as the excellent book [51], where many more references may be found. Group valued moment maps are discussed in [45] for S1”