9 papers · 1 filter
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…
The relation between local and global dual pairs
James Montaldi, Juan-Pablo Ortega, Tudor S. Ratiu
In this note we clarify the relationship between the local and global definitions of dual pairs in Poisson geometry. It turns out that these are not equivalent. For the passage fro…
Optimal reduction
Juan-Pablo Ortega
We generalize various symplectic reduction techniques to the context of the optimal momentum map. Our approach allows the construction of symplectic point and orbit reduced spaces…
The symplectic reduced spaces of a Poisson action
Juan-Pablo Ortega
During the last thirty years, symplectic or Marsden--Weinstein reduction has been a major tool in the construction of new symplectic manifolds and in the study of mechanical system…