MiS Preprint Repository

We show that there exists a lipschitz almost-complex structure on $\mathbf{C}{P}^2$, arbitrary close to the standard one, for which there exists a compact lamination by $J$-holomorphic curves satisfying the following properties: it is minimal, it has hyperbolic holonomy and it is transversally lipschitz. Its transverse Hausdorff dimension can be any number $\delta$ in the interval $(0,{\delta }_{max})$, where ${\delta }_{max}=1.6309..$. We also show that there exists a compact lamination by totally real surfaces in ${\mathbf{C}}^2$ with the same properties. Our laminations are transversally totally disconnected, and for this reason are called solenoids.