In those branches of mathematics called dynamical systems and ergodic theory, the concept of a **wandering set** formalizes a certain idea of movement and mixing in such systems. When a dynamical system has a wandering set of non-zero measure, then the system is a dissipative system. This is very much the opposite of a conservative system, for which the ideas of the Poincaré recurrence theorem apply. Intuitively, the connection between wandering sets and dissipation is easily understood: if a portion of the phase space "wanders away" during normal time-evolution of the system, and is never visited again, then the system is dissipative. The language of wandering sets can be used to give a precise, mathematical definition to the concept of a dissipative system. The notion of wandering sets in phase space was introduced by Birkhoff in 1927.

Read more about Wandering Set: Wandering Points, Non-wandering Points, Wandering Sets and Dissipative Systems

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### Famous quotes containing the words set and/or wandering:

“Colleges, in like manner, have their indispensable office,—to teach elements. But they can only highly serve us, when they aim not to drill, but to create; when they gather from far every ray of various genius to their hospitable halls, and, by the concentrated fires, *set* the hearts of their youth on flame.”

—Ralph Waldo Emerson (1803–1882)

“It is a thorny undertaking, and more so than it seems, to follow a movement so *wandering* as that of our mind, to penetrate the opaque depths of its innermost folds, to pick out and immobilize the innumerable flutterings that agitate it. And it is a new and extraordinary amusement, which withdraws us from the ordinary occupations of the world, yes, even from those most recommended.”

—Michel de Montaigne (1533–1592)