Karl Jones: Created page with "In mathematics, a '''flow''' formalizes the idea of the motion of particles in a fluid. == Description == Flows are ubiquitous in science, including engineering..."

2016-09-22T14:35:31Z

Created page with "In mathematics, a '''flow''' formalizes the idea of the motion of particles in a fluid. == Description == Flows are ubiquitous in science, including engineering..."

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In [[mathematics]], a '''flow''' formalizes the idea of the motion of particles in a fluid.

== Description ==

Flows are ubiquitous in [[science]], including [[engineering]] and [[physics]]. The notion of flow is basic to the study of [[Ordinary differential equation|ordinary differential equations]].

Informally, a flow may be viewed as a continuous motion of points over time. More formally, a flow is a [[group action]] of the real numbers 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 group|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]].

Flows may also be defined for systems of random variables and stochastic processes, and occur in the study of ergodic dynamical systems.

The most celebrated of these is perhaps the [[Bernoulli flow]].

== See also ==

* [[Abel equation]]
* [[Infinite compositions of analytic functions]]
* [[Iterated function]]
* [[Ordinary differential equation]]
* [[Schröder's equation]]

== External links ==

[[Category:Mathematics]]

Flow (mathematics) - Revision history

Karl Jones: Created page with "In mathematics, a '''flow''' formalizes the idea of the motion of particles in a fluid. == Description == Flows are ubiquitous in science, including engineering..."