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.
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08 Aug 1996
TL;DR: A survey of open problems in symplectic integration by R. I. McLachlan and C. Koseleff can be found in this paper, along with an exhaustive search of symplectic integrators using computer algebra.
Abstract: Formulation of a new class of fractional-step methods for the incompressible MHD equations that retains the long-term dissipativity of the continuum.. by F. Armero and J. Simo Symplectic methods for conservative multibody systems by E. J. Barth and B. J. Leimkuhler An introduction to symplectic integrators by P. J. Channell and F. R. Neri Symplectic maps and computation of orbits in particle accelerators by A. J. Dragt and D. T. Abell Amold diffusion in symplectic lattice maps by D. J. D. Earn and A. Lichtenberg Integrable Hamiltonians from close approximations to invariant tori by M. Kaasalainen and J. Binney Exhaustive search of symplectic integrators using computer algebra by P. V. Koseleff Conserving algorithms for the $N$ dimensional rigid body by D. K. Lewis and J. Simo More on symplectic correctors by R. I. McLachlan A survey of open problems in symplectic integration by R. I. McLachlan and C. Scovel Symplectic integrators for systems of rigid bodies by S. Reich Backward error analysis of symplectic integrators by J. M. Sanz-Serna Numerical determination of caustics and their bifurcations by T. J. Stuchi and R. Vieira-Martins Symplectic correctors by J. Wisdom, M. Holman, and J. Touma.
61 citations
TL;DR: In this article, it was shown that if B is a polynomial ring over a field, then for r ≥ 2, any element of Sp2rB can be written as a product of elementary symplectic matrices over B.
Abstract: We prove that if B is a polynomial ring over a field, then for r ≥ 2, any element of Sp2rB can be written as a product of elementary symplectic matrices over B. We also prove a stabilization theorem for the symplectic K1-functor in the case of polynomial rings and Laurent rings. Bibliography: 6 titles.
61 citations
TL;DR: In this paper, it was shown that the circle action must be Hamiltonian, and M must have the equivariant cohomology and Chern classes of (P1)n.
61 citations
TL;DR: In this paper, it was shown that there is a twistor-like correspondence between Finsler metrics on ΩPn whose geodesics are projective lines and a class of symplectic forms on the Grassmannian of 2-planes in ℩n+1.
Abstract: Inspired by Hofer's definition of a metric on the space of compactly supported Hamiltonian maps on a symplectic manifold, this paper exhibits an area-length duality between a class of metric spaces and a class of symplectic manifolds. Using this duality, it is shown that there is a twistor-like correspondence between Finsler metrics on ℝPn whose geodesics are projective lines and a class of symplectic forms on the Grassmannian of 2-planes in ℝn+1.
60 citations
TL;DR: In this article, the Symplectic ideals of poisson algebras and the poisson structure associated to quantum matrices are discussed, and a poisson algebraic model is proposed.
Abstract: (1999). Symplectic ideals of poisson algebras and the poisson structure associated to quantum matrices. Communications in Algebra: Vol. 27, No. 5, pp. 2163-2180.
60 citations