%0 Journal Article
%T Divergence of Morse geodesics
%A Hung Cong Tran
%J Mathematics
%D 2014
%I arXiv
%R 10.1007/s10711-015-0107-3
%X Behrstock and Dru\c{t}u raised a question about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. In this paper, we answer the question of Behrstock and Dru\c{t}u by showing that for each real number $s\geq 2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.
%U http://arxiv.org/abs/1408.6089v2