Institute for Mathematical Sciences

Preprint ims08-05

Jeremy Kahn, Mikhail Lyubich, and Lasse Rempe
A note on hyperbolic leaves and wild laminations of rational functions

Abstract: We study the affine orbifold laminations that were constructed in \cite{mishayair}. An important question left open in \cite{mishayair} is whether these laminations are always locally compact. We show that this is not the case.

The counterexample we construct has the property that the \emph{regular leaf space} contains (many) hyperbolic leaves that intersect the Julia set; whether this can happen is itself a question raised in \cite{mishayair}.

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