Difference between revisions of "Nil flow"
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| − | A flow on a [[Nil manifold|nil manifold]] | + | <!-- |
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| + | A flow on a [[Nil manifold|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==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> L. Auslander, L. Green, F. Hahn, "Flows on homogeneous spaces" , Princeton Univ. Press (1963)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> L. Auslander, L. Green, F. Hahn, "Flows on homogeneous spaces" , Princeton Univ. Press (1963)</TD></TR></table> | ||
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====Comments==== | ====Comments==== | ||
The first example of a compact minimal flow that is distal but not equicontinuous was a nil flow (cf. [[Distal dynamical system|Distal dynamical system]]; [[Equicontinuity|Equicontinuity]]). | The first example of a compact minimal flow that is distal but not equicontinuous was a nil flow (cf. [[Distal dynamical system|Distal dynamical system]]; [[Equicontinuity|Equicontinuity]]). | ||
Latest revision as of 08:02, 6 June 2020
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).
How to Cite This Entry:
Nil flow. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Nil_flow&oldid=47972
Nil flow. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Nil_flow&oldid=47972
This article was adapted from an original article by D.V. Anosov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article