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Suspension (dynamical systems) : ウィキペディア英語版
Suspension (dynamical systems)

Suspension is a construction passing from a map to a flow. Namely, let X be a metric space, f:X\to X be a continuous map and r:X\to\mathbb^+ be a function (roof function or ceiling function) bounded away from 0. Consider the quotient space
:X_r=\/(x,r(x))\sim(fx,0).
The suspension of (X,f) with roof function r is the semiflow〔M. Brin and G. Stuck, ''Introduction to Dynamical Systems'', Cambridge University Press, 2002.〕 f_t:X_r\to X_r induced by the time-translation T_t:X\times\mathbb\to X\times\mathbb, (x,s)\mapsto (x,s+t).
If r(x)\equiv 1, then the quotient space is also called the mapping torus of (X,f).
==References==



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