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.
Department of Mathematics, The Weizmann Institute of Science, 234 Herzl Street, Rehovot 7610001, Israel
Bibliografia
[1] Dmitri Burago, Yuri Burago, and Sergei Ivanov, A Course in Metric Geometry, Graduate Studies inMathematics, 33. American Mathematical Society (2001).
[2] Kate Juschenko and Nicolas Monod, Cantor systems, piecewise translations and simple amenable groups. Annals ofMathematics 2 (2013), 775–787. [WoS]
[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.