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This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Flow_(mathematics)


00:00:38 1 Formal definition
00:01:17 1.1 Alternative notations
00:01:56 2 Orbits
00:02:35 3 Examples
00:03:14 3.1 Autonomous systems of ordinary differential equations
00:03:33 3.2 Time-dependent ordinary differential equations
00:04:12 3.3 Flows of vector fields on manifolds
00:06:08 3.4 Solutions of heat equation
00:06:47 3.5 Solutions of wave equation
00:08:24 3.6 Bernoulli flow
00:10:40 4 See also
00:11:19 5 References
00:11:58 See also



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SUMMARY
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In mathematics, a flow formalizes the idea of the motion of particles in a fluid. Flows are ubiquitous in science, including engineering and physics. The notion of flow is basic to the study of 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 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.