  Let $f: \mathbb{T}^3\to\mathbb{T}^3$ be a partially hyperbolic diffeomorphism
on the 3-torus $\mathbb{T}^3$. In his thesis, Hammerlindl proved that for
lifted center foliation $\mathcal{F}^c_f$, there exists $R>0$, such that for
any $x\in \mathbb{R}^3$, ${\cal F}^c_f(x)\subset B_R (x+E^c)$, where
$\mathbb{R}^3=E^s\oplus E^c\oplus E^u$ is the partially hyperbolic splitting of
the linear model of $f$. The same is true for the lifted center-stable and
center-unstable foliations. Then he asked if the this property is true for
strong stable and strong unstable foliations. In this note, we give a negative
answer to Hammerlindl's question.

Dynamical Systems