  We consider here the family of semilinear parabolic problems
\begin{equation*} \begin{array}{rcl} \left\{ \begin{array}{rcl}
u_t(x,t)&=&\Delta u(x,t) -au(x,t) + f(u(x,t)) ,\,\,\ x \in \Omega_\epsilon
\,\,\,\mbox{and}\,\,\,\,\,\,t>0\,, \\ \displaystyle\frac{\partial u}{\partial
N}(x,t)&=&g(u(x,t)), \,\, x \in \partial\Omega_\epsilon
\,\,\,\mbox{and}\,\,\,\,\,\,t>0\,, \end{array} \right. \end{array}
\end{equation*} where $ {\Omega} $ is the unit square,
$\Omega_{\epsilon}=h_{\epsilon}(\Omega)$ and $h_{\epsilon}$ is a family of
diffeomorphisms converging to the identity in the $C^1$-norm. We show that the
problem is well posed for $\epsilon>0$ sufficiently small in a suitable phase
space, the associated semigroup has a global attractor $\mathcal{A}_{\epsilon}$
and the family $\{\mathcal{A}_{\epsilon}\}$ is continuous at $\epsilon = 0$.
