Nil flow

A flow on a nil manifold $ M = G / H $ defined by the action on $ M $ of some one-parameter subgroup $ g _ {t} $ of a nilpotent Lie group $ G $: If $ M $ consists of the cosets $ g H $, then under the action of the nil flow such a coset at time $ t $ goes over in $ g _ {t} g H $.

References

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

Comments

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