Almost-holomorphic and totally real solenoids in complex surfaces

Bertrand Deroin

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Submission date: 07. Jan. 2005 (revised version: January 2005)
Pages: 24
Bibtex
MSC-Numbers: 37F75, 37C85, 53D05, 37B50, 35B41
Keywords and phrases: solenoid, branched surfaces, pseudo-holomorphic curves, totally real surfaces
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Abstract:
We show that there exists a lipschitz almost-complex structure on , 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 in the interval , where . We also show that there exists a compact lamination by totally real surfaces in with the same properties. Our laminations are transversally totally disconnected, and for this reason are called solenoids.