  In this work we study fractal properties of rough differential equations
driven by a fractional Brownian motions with Hurst parameter $H>\frac{1}{4}$.
In particular, we show that the Hausdorff dimension of the sample paths of the
solution is $\min\{d,\frac{1}{H}\}$ and that the Hausdorff dimension of the
level set $L_x=\{ t\in[\epsilon,1]: X_t=x\}$ is $1-dH$ with positive
probability when $d<\frac{1}{H}$
