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Reversible dynamics : ウィキペディア英語版
Reversible dynamics

== Mathematics ==
In mathematics, a dynamical system is invertible if the forward evolution is one-to-one, not many-to-one; so that for every state there exists a well-defined reverse-time evolution operator.
The dynamics are time-reversible if there exists a transformation (an involution) π which gives a one-to-one mapping between the time-reversed evolution of any one state, and the forward-time evolution of another corresponding state, given by the operator equation:
:U_ = \pi \, U_\, \pi
Any time-independent structures (for example critical points, or attractors) which the dynamics gives rise to must therefore either be self-symmetrical or have symmetrical images under the involution π.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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