Bi-Lipschitz bijections of $\mathbb{Z}$

Alexander Shamov; Itai Benjamini

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Bi-Lipschitz bijections of $\mathbb{Z}$

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arxiv 1509.07670 v1 pith:JCKWTUYQ submitted 2015-09-25 math.MG

Itai Benjamini , Alexander Shamov This is my paper · ORCID

classification math.MG

keywords bi-lipschitzbijectionsmathbbactionbijectionboundedcommentdistance

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abstract

It is shown that every bi-Lipschitz bijection from $\mathbb{Z}$ to itself is at a bounded $L_{\infty}$ distance from either the identity or the reflection. We then comment on the group-theoretic properties of the action of bi-Lipschitz bijections.

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