Let $T^2$ be a 2-torus and $f:T^2\rightarrow T^2$ a smooph map. Let $f_*:\pi_1(T^2)\rightarrow\pi_1(T^2)$ be the iducend map in the fudamental group $\pi_1$. If $f_*$ has no eigenvalue greater than 1, then all ball of T ^ 2 has subexponential growth by $ f $. Why?