Cosmological phase space of R^n gravity

We present some exact solutions and a phase space analysis of metric $f(R)$-gravity models of the type $R^n$. We divide our discussion in $n\mathrm{\ne }2$ and $n=2$ models. The later model is a good approximation, at late times to the $f(R)=\frac{2}{\pi }R{\tan }^{-1}(R\mathrm{/}{\beta }^2)$ gravity model, being this an example of a non–singular case. For $n\mathrm{\ne }2$ models we have found power law solutions for the scale factor that are attractors and that comply with WMAP 5-years data if $n<-2.55$ or $1.67<n<2$. On the other hand, the quadratic model has the de Sitter solution as an attractor, that also complies with WMAP 5-years data.