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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.


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Journal ArticleDOI
TL;DR: In this paper, the multiplicity of closed characteristics on partially symmetric convex compact hypersurfaces in R 2n was studied and the main ingredient of the proof is a new (P,ω)-index function and its iteration theory for symplectic matrix paths and some symplectic orthogonal matrix P.

32 citations

Journal ArticleDOI
TL;DR: In this article, a conjecture on fixed points of a closed symplectic manifold generalizing the "Poincare geometric theorem" was formulated, which gives a lower bound for the number of critical points on a function on this manifold.
Abstract: Symplectic topology arose with [I], where a conjecture on fixed points of symplectomorphisms generalizing the "Poincare geometric theorem" [2, 3] was formulated. This conjecture of Arnol'd gives as a lower bound for the number of fixed points of symplectomorphis which is a homologicai identity of a closed symplectic manifold* the minimal number of critical points of a function on this manifold. The present paper is basically devoted to a discussion of the following conjecture.

32 citations

Journal ArticleDOI
TL;DR: A theorem analogous to the Weyl branching law for the unimodular groups is derived for Sp(2n) in this article, which is the case for all the groups in this paper.
Abstract: A theorem analogous to the Weyl branching law for the unimodular groups is derived for Sp(2n).

32 citations

Journal ArticleDOI
TL;DR: In this article, the Frechet space of tamed almost complex structures as defined by the given symplectic form has an open and dense subset whose complex structures are compatible with respect to a co-occurrence form that is cohomologous to the given one.
Abstract: Fix a compact 4-dimensional manifold with self-dual second Betti number one and with a given symplectic form. This article proves the following: The Frechet space of tamed almost complex structures as defined by the given symplectic form has an open and dense subset whose complex structures are compatible with respect to a symplectic form that is cohomologous to the given one. The theorem is proved by constructing the new symplectic form by integrating over a space of currents that are defined by pseudo-holomorphic curves.

32 citations

01 Jan 2007
TL;DR: In this paper, the expectation values for quantized linear symplectic maps on the multidimensional torus and their distribu- tion in the semiclassical limit were studied.
Abstract: We look at the expectation values for quantized linear symplectic maps on the multidimensional torus and their distribu- tion in the semiclassical limit. We construct super-scars that are stable under the arithmetic symmetries of the system and localize on invariant manifolds. We show that these super-scars exist only when there are isotropic rational subspaces, invariant under the linear map. In the case where there are no such scars, we com- pute the variance of the fluctuations of the matrix elements for the desymmetrized system, and present a conjecture for their limiting distributions.

31 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202310
202221
202113
20208
201910
201818