Surfaces branchées et solénoïdes $ε$-holomorphes

Mathematics – Dynamical Systems

Scientific paper

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22 pages, 9 figures

Scientific paper

We show that for every $\epsilon>0$, there exists a compact lamination by $\epsilon$-holomorphic surfaces in the complex projective plane, minimal, and that carries hyperbolic holonomy. We call $\epsilon$-holomorphic a real 2-dimensional surface $\Sigma$ in ${\bf C}P^2$ such that the angle between $T\Sigma$ and $iT\Sigma$ is uniformly bounded by $\epsilon$. When $\epsilon$ is sufficiently small, such surfaces are in particular symplectic.

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