It is shown that every bi-Lipschitz bijection from Z to itself is at a bounded L1 distance from either the identity or the reflection.We then comment on the group-theoretic properties of the action of bi-Lipschitz bijections.
@article{bwmeta1.element.doi-10_1515_agms-2015-0018,
author = {Itai Benjamini and Alexander Shamov},
title = {Bi-Lipschitz Bijections of Z},
journal = {Analysis and Geometry in Metric Spaces},
volume = {3},
year = {2015},
zbl = {1325.26011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0018}
}
Itai Benjamini; Alexander Shamov. Bi-Lipschitz Bijections of Z. Analysis and Geometry in Metric Spaces, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0018/
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