87 citations · 877 across the 97 of their papers we have counts for
9 papers · 1 filter
A Class of Integrable Geodesic Flows on the Symplectic Group and the Symmetric Matrices
Anthony M. Bloch, Arieh Iserles, Jerrold E. Marsden +1
This paper shows that the left-invariant geodesic flow on the symplectic group relative to the Frobenius metric is an integrable system that is not contained in the Mishchenko-Fome…
Openness and convexity for momentum maps
Petre Birtea, Juan-Pablo Ortega, Tudor S. Ratiu
The purpose of this paper is finding the essential attributes underlying the convexity theorems for momentum maps. It is shown that they are of topological nature; more specificall…
Cotangent bundle reduction
Juan-Pablo Ortega, Tudor S. Ratiu
This encyclopedia article briefly reviews without proofs some of the main results in cotangent bundle reduction. The article recalls most the necessary prerequisites to understand…
Poisson reduction
Juan-Pablo Ortega, Tudor S. Ratiu
This encyclopedia article briefly reviews without proofs some of the main results in Poisson reduction. The article recalls most the necessary prerequisites to understand the main…
Symmetry and symplectic reduction
Juan-Pablo Ortega, Tudor S. Ratiu
This encyclopedia article briefly reviews without proofs some of the main results in symplectic reduction. The article recalls most the necessary prerequisites to understand the ma…
Singular cosphere bundle reduction
Oana Dragulete, Tudor S. Ratiu, Miguel Rodriguez-Olmos
This paper studies singular contact reduction for cosphere bundles at the zero value of the momentum map. A stratification of the singular quotient, finer than the contact one and…
The Lie-Poisson structure of the LAE- equation
François Gay-Balmaz, Tudor S. Ratiu
This paper shows that the time map of the averaged Euler equations, with Dirichlet, Neumann, and mixed boundary conditions is canonical relative to a Lie-Poisson bracket constr…
The reduced spaces of a symplectic Lie group action
Juan-Pablo Ortega, Tudor S. Ratiu
There exist three main approaches to reduction associated to canonical Lie group actions on a symplectic manifold, namely, foliation reduction, introduced by Cartan, Marsden-Weinst…
Geometric representation theory for unitary groups of operator algebras
Daniel Beltiţă, Tudor S. Ratiu
Geometric realizations for the restrictions of GNS representations to unitary groups of -algebras are constructed. These geometric realizations use an appropriate concept of r…