Exponential decay of correlations for a real valued dynamical system embedded in ${\mathbb{R}}^2$

We study the real valued process $\{X_t,t\in \mathbb{N}\}$ defined by $X_{t+2}=\phi (X_t,X_{t+1})$, where the $X_t$ are bounded. We aim at proving the decay of correlations for this model, under regularity assumptions on the transformation $\phi$.