Wandering Set

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 SetWandering Points, Non-wandering Points, Wandering Sets and Dissipative Systems

Other articles related to "wandering set, wandering, set":

Axiom A - Properties
... case, the whole manifold M is hyperbolic (although it is an open question whether the non-wandering set Ω(f) constitutes the whole M) ... Rufus Bowen showed that the non-wandering set Ω(f) of any axiom A diffeomorphism supports a Markov partition ... The density of the periodic points in the non-wandering set implies its local maximality there exists an open neighborhood U of Ω(f) such that ...
Wandering Sets and Dissipative Systems
... A wandering set is a collection of wandering points ... More precisely, a subset W of is a wandering set under the action of a discrete group if W is measurable and if, for any the intersection is a set of measure zero ... The concept of a wandering set is in a sense dual to the ideas expressed in the Poincaré recurrence theorem ...

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