Superdiffusive limits for deterministic fast-slow dynamical systems

We consider deterministic fast-slow dynamical systems on $$\mathbb{R}$^m\times Y$ of the form $$\{\begin{array}{l}{x}_{k+1}^{(n)}=x_k^{(n)}+n^{-1}a(x_k^{(n)})+n^{-1\mathrm{/}\alpha }b(x_k^{(n)})v(y_k),y_{k+1}=f(y_k),\end{array}$$ where $\alpha \in (1,2)$. Under certain assumptions we prove convergence of the $m$-dimensional process $X_n(t)= x_{\lfloor nt \rfloor}^{(n)}$ to the solution of the stochastic differential equation $$\text{\hspace{0.17em}⁣}\mathrm{d}X=a(X)\text{\hspace{0.17em}⁣}\mathrm{d}t+b(X)\diamond \text{\hspace{0.17em}⁣}\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.