4 papers · 1 filter
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…
The optimal momentum map
Juan-Pablo Ortega, Tudor S. Ratiu
The presence of symmetries in a Hamiltonian system usually implies the existence of conservation laws that are represented mathematically in terms of the dynamical preservation of…
Singular dual pairs
Juan-Pablo Ortega
We generalize the notions of dual pair and polarity introduced by S. Lie and A. Weinstein in order to accommodate very relevant situations where the application of these ideas is d…