Suspension (dynamical systems)

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Suspension is a construction passing from a map to a flow. Namely, let be a metric space, be a continuous map and be a function (roof function or ceiling function) bounded away from 0. Consider the quotient space

The suspension of with roof function is the semiflow[1] induced by the time translation .

If , then the quotient space is also called the mapping torus of .

References[edit]

  1. ^ M. Brin and G. Stuck, Introduction to Dynamical Systems, Cambridge University Press, 2002.