Topic
Symplectic vector space
About: Symplectic vector space is a research topic. Over the lifetime, 2048 publications have been published within this topic receiving 53456 citations.
Papers published on a yearly basis
Papers
More filters
Journal Article•
TL;DR: In this paper, the authors present a legal analysis of the agreement between the Scuola Normale Superiore di Pisa (SNSN) and the National Archives of Italy.
Abstract: © Scuola Normale Superiore, Pisa, 1992, tous droits réservés. L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
17 citations
TL;DR: In this article, the authors studied the rigidity and flexibility of symplectic embeddings in the model case in which the domain is a symplectic ellipsoid and showed that any connected symplectic 4-manifold of finite volume can be asymptotically filled with skinny ellipoids.
Abstract: We study the rigidity and flexibility of symplectic embeddings in the model case in which the domain is a symplectic ellipsoid. It is first proved that under the conditionrn2≤2r12 the symplectic ellipsoidE(r1,…,rn)with radiir1≤…≤rndoes not symplectically embed into a ball of radius strictly smaller thanrn.We then use symplectic folding to see that this condition is sharp. We finally sketch a proof of the fact that any connected symplectic 4-manifold of finite volume can be asymptotically filled with skinny ellipoids.
17 citations
TL;DR: An isomorphism between the Lobachevsky and de Sitter world geometries with the symplectic geometry and the Lie algebra of binary quadratic forms was used to derive the altitudes concurrence for the Lipschitz triangle as mentioned in this paper.
17 citations
TL;DR: In this paper, the authors studied the general case of a lifted action that does not admit a momentum map and used its natural generalization, a cylinder valued momentum map introduced by Condevaux et al.
Abstract: There exist three main approaches to reduction associated to canonical Lie group actions on a symplectic manifold, namely, foliation reduction, introduced by Cartan, Marsden-Weinstein reduction, and optimal reduction, introduced by the authors. When the action is free, proper, and admits a momentum map these three approaches coincide. The goal of this paper is to study the general case of a symplectic action that does not admit a momentum map and one needs to use its natural generalization, a cylinder valued momentum map introduced by Condevaux et al. In this case it will be shown that the three reduced spaces mentioned above do not coincide, in general. More specifically, the Marsden-Weinstein reduced spaces are not symplectic but Poisson and their symplectic leaves are given by the optimal reduced spaces. Foliation reduction produces a symplectic reduced space whose Poisson quotient by a certain Lie group associated to the group of symmetries of the problem equals the Marsden-Weinstein reduced space. We illustrate these constructions with concrete examples, special emphasis being given to the reduction of a magnetic cotangent bundle of a Lie group in the situation when the magnetic term ensures the non-existence of the momentum map for the lifted action. The precise relation of the cylinder valued momentum map with group valued momentum maps for Abelian Lie groups is also given.
17 citations