Deterministic Nonperiodic Flow


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An example of deterministic chaotic dynamics. Such systems cannot be predicted unless the initial or boundary conditions are known exactly which is FAPP impossible. The most recent era in which chaotic dynamics was studied was initiated by a meteorologist, Ed Lorenz, who used a set of non-linear differential equations to model atmospheric convection. He noticed (to his surprise) that when he started the solution iteration with initial conditions that were very nearly equal he ended up with totally different solutions.

An earlier, pre-computer era was started by the French mathematician Henri Poincare who discovered that the trajectories of planets in the solar system were part of a chaotic system who long term behavior could not be predicted. In 1905 Poincare made some qualitative studies, but was unable to follow it up in detail because hand calculation was infeasible.

Ba'al Chatzaf

Edited by BaalChatzaf
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