Flow

In mathematics, a flow formalizes, in mathematical terms, the general idea of "a variable that depends on time" that occurs very frequently in engineering, physics and the study of ordinary differential equations. Informally, if x(t) is some coordinate of some system that behaves continuously as a function of t, then x(t) is a flow. More formally, a flow is the group action of a one-parameter group on a set.

The idea of a vector flow, that is, the flow determined by a vector field, occurs in the areas of differential topology, Riemannian geometry and Lie groups. Specific examples of vector flows include the geodesic flow, the Hamiltonian flow, the Ricci flow, the mean curvature flow, and the Anosov flow.