Cubic Polynomial Maps with Periodic Critical Orbit, Part II: Escape Regions

2009/10/09 by Bonifant, Araceli, Kiwi, Jan, Milnor, John · 1 citation
#30C10 #30D05 #37F10 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.0910.1866

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 will 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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