On the entropy norm on $Ham(S^2)$

Michael Brandenbursky, Egor Shelukhin

Published 2019-09-12Version 1

In this note we prove that for each positive integer $m$ there exists a bi-Lipschitz embedding $Z^m\to Ham(S^2)$, where $Ham(S^2)$ is equipped with the entropy metric. In particular, the same result holds when the entropy metric is substituted with the autonomous metric.