Nil flow

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A flow on a nil manifold defined by the action on of some one-parameter subgroup of a nilpotent Lie group : If consists of the cosets , then under the action of the nil flow such a coset at time goes over in .


[1] L. Auslander, L. Green, F. Hahn, "Flows on homogeneous spaces" , Princeton Univ. Press (1963)


The first example of a compact minimal flow that is distal but not equicontinuous was a nil flow (cf. Distal dynamical system; Equicontinuity).

How to Cite This Entry:
Nil flow. D.V. Anosov (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098