**Symplectic** — Sym*plec tic, a. [Gr. ? plaiting together, fr. ? to plait together.] (Anat.) Plaiting or joining together; said of a bone next above the quadrate in the mandibular suspensorium of many fishes, which unites together the other bones of the… … The Collaborative International Dictionary of English

**Symplectic geometry** — is a branch of differential topology/geometry which studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2 form. Symplectic geometry has its origins in the Hamiltonian formulation of classical… … Wikipedia

**Symplectic sum** — In mathematics, specifically in symplectic geometry, the symplectic sum is a geometric modification on symplectic manifolds, which glues two given manifolds into a single new one. It is a symplectic version of connected summation along a… … Wikipedia

**Symplectic manifold** — In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2 form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology.… … Wikipedia

**Symplectic vector space** — In mathematics, a symplectic vector space is a vector space V equipped with a nondegenerate, skew symmetric, bilinear form omega; called the symplectic form. Explicitly, a symplectic form is a bilinear form omega; : V times; V rarr; R which is *… … Wikipedia

**Symplectic cut** — In mathematics, specifically in symplectic geometry, the symplectic cut is a geometric modification on symplectic manifolds. Its effect is to decompose a given manifold into two pieces. There is an inverse operation, the symplectic sum, that… … Wikipedia

**Symplectic group** — For finite groups with all characteristc abelian subgroups cyclic, see group of symplectic type. Group theory … Wikipedia

**Symplectic matrix** — In mathematics, a symplectic matrix is a 2n times; 2n matrix M (whose entries are typically either real or complex) satisfying the condition:M^T Omega M = Omega,.where MT denotes the transpose of M and Omega; is a fixed nonsingular, skew… … Wikipedia

**Symplectic vector field** — In physics and mathematics, a symplectic vector field is one whose flow preserves a symplectic form. That is, if (M,omega) is a symplectic manifold, then a vector field Xinmathfrak{X}(M) is symplectic if its flow preserves the symplectic… … Wikipedia

**Symplectic integrator** — In mathematics, a symplectic integrator (SI) is a numerical integration scheme for a specific group of differential equations related to classical mechanics and symplectic geometry. Symplectic integrators form the subclass of geometric… … Wikipedia