  We consider deterministic fast-slow dynamical systems on $\mathbb{R}^m\times
Y$ of the form \[
  \begin{cases}
  x_{k+1}^{(n)} = x_k^{(n)} + n^{-1} a(x_k^{(n)}) + n^{-1/\alpha} b(x_k^{(n)})
v(y_k)\;,\quad
  y_{k+1} = f(y_k)\;,
  \end{cases} \] where $\alpha\in(1,2)$. Under certain assumptions we prove
convergence of the $m$-dimensional process $X_n(t)=
  x_{\lfloor nt \rfloor}^{(n)}$ to the solution of the stochastic differential
equation \[
  \mathop{}\!\mathrm{d} X = a(X)\mathop{}\!\mathrm{d} t + b(X) \diamond
\mathop{}\!\mathrm{d} L_\alpha
  \; ,
  \] where $L_\alpha$ is an $\alpha$-stable L\'evy process and $\diamond$
indicates that the stochastic integral is in the Marcus sense. In addition, we
show that our assumptions are satisfied for intermittent maps $f$ of
Pomeau-Manneville type.
