2 research outputs found
Cubic Polynomial Maps with Periodic Critical Orbit, Part II: Escape Regions
The parameter space for monic centered cubic polynomial maps
with a marked critical point of period is a smooth affine algebraic curve
whose genus increases rapidly with . Each 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 will describe the topology of
, and of its smooth compactification, in terms of these escape
regions. It concludes with a discussion of the real sub-locus of
.Comment: 51 pages, 16 figure