Bi-Lipschitz Bijections of Z

Itai Benjamini; Alexander Shamov

Analysis and Geometry in Metric Spaces (2015)

  • Volume: 3, Issue: 1, page 313-316, electronic only
  • ISSN: 2299-3274

Abstract

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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.

How to cite

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Itai Benjamini, and Alexander Shamov. "Bi-Lipschitz Bijections of Z." Analysis and Geometry in Metric Spaces 3.1 (2015): 313-316, electronic only. <http://eudml.org/doc/276007>.

@article{ItaiBenjamini2015,
abstract = {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.},
author = {Itai Benjamini, Alexander Shamov},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Bi-Lipschitz; bijections; bi-Lipschitz},
language = {eng},
number = {1},
pages = {313-316, electronic only},
title = {Bi-Lipschitz Bijections of Z},
url = {http://eudml.org/doc/276007},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Itai Benjamini
AU - Alexander Shamov
TI - Bi-Lipschitz Bijections of Z
JO - Analysis and Geometry in Metric Spaces
PY - 2015
VL - 3
IS - 1
SP - 313
EP - 316, electronic only
AB - 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.
LA - eng
KW - Bi-Lipschitz; bijections; bi-Lipschitz
UR - http://eudml.org/doc/276007
ER -

References

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  1. [1] Dmitri Burago, Yuri Burago, and Sergei Ivanov, A Course in Metric Geometry, Graduate Studies inMathematics, 33. American Mathematical Society (2001).  
  2. [2] Kate Juschenko and Nicolas Monod, Cantor systems, piecewise translations and simple amenable groups. Annals ofMathematics 2 (2013), 775–787. [WoS] Zbl1283.37011
  3. [3] Kate Juschenko and Mikael de la Salle, Invariant means for the wobbling group. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 2, 281–290.  Zbl1322.43001

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