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wandering set

名詞

wandering set (複数形 wandering sets)

  1. (mathematics) In dynamical systems and ergodic theory, a formalization of a certain idea of movement and mixing.

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ウィキペディア英語版

出典:Wikipedia

Wandering set

出典:『Wikipedia』 (2010/11/23 04:25 UTC 版)

英語による解説

ウィキペディア英語版からの引用
引用

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.

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