Explore: Symplectic Spaces

In mathematics, a symplectic vector space is a vector space V {\displaystyle V} over a field F {\displaystyle F} (for example the real numbers R {\displaystyle

A symplectic space may refer to: Symplectic manifold Symplectic vector space This disambiguation page lists articles associated with the title Symplectic

algebra Symplectic integrator Symplectic manifold Symplectic matrix Symplectic representation Symplectic vector space, a vector space with a symplectic bilinear

Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds

\omega } , called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology. Symplectic manifolds arise naturally

notion of Poisson manifold generalises that of symplectic manifold, which in turn generalises the phase space from Hamiltonian mechanics. A Poisson structure

vector spaces. The abstract analog of a symplectic matrix is a symplectic transformation of a symplectic vector space. Briefly, a symplectic vector space (

represents a transformation of phase space that is volume-preserving and preserves the symplectic structure of phase space, and is called a canonical transformation

hypercomplex manifold Quaternion-Kähler manifold Symplectic topology Symplectic space Symplectic manifold Symplectic structure Symplectomorphism Contact structure

the parent space which retains the same structure. While modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological