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MiS Preprint
3/2005
Almost-holomorphic and totally real solenoids in complex surfaces
Bertrand Deroin
Abstract
We show that there exists a lipschitz almost-complex structure on ${\bf C}P^2$, 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 ${\bf C}^2$ with the same properties. Our laminations are transversally totally disconnected, and for this reason are called solenoids.
