## Institute for Mathematical Sciences

## Preprint ims09-03

** Araceli Bonifant, Jan Kiwi, John Milnor**
*Cubic polynomial maps with periodic critical orbit, Part II: Escape regions*

Abstract: The parameter space S_p for monic centered cubic polynomial maps with a marked critical point of period p is a smooth affine algebraic curve
whose genus increases rapidly with p. Each S_p consists of a compact
connectedness locus together with finitely many escape regions, each of
which is biholomorphic to a punctured disk and is characterized by an
essentially unique Puiseux series. This note with describe the topology
of S_p, and of its smooth compactification, in terms of these escape
regions. It concludes with a discussion of the real sub-locus of S_p.

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