Cubic polynomial maps with periodic critical orbit, Part II: Escape regions

Authors:
Araceli Bonifant, Jan Kiwi and John Milnor

Journal:
Conform. Geom. Dyn. **14** (2010), 68-112

MSC (2010):
Primary 37F10, 30C10, 30D05

DOI:
https://doi.org/10.1090/S1088-4173-10-00204-3

Published electronically:
March 9, 2010

Erratum:
Conform. Geom. Dyn. 14 (2010), 190-193.

MathSciNet review:
2600536

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Abstract | References | Similar Articles | Additional Information

Abstract: 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. In particular, it computes the Euler characteristic. It concludes with a discussion of the real sub-locus of .

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Additional Information

**Araceli Bonifant**

Affiliation:
Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881

Email:
bonifant@math.uri.edu

**Jan Kiwi**

Affiliation:
Facultad de Matemáticas, Pontificia Universidad Católica, Casilla 306, Correo 22, Santiago de Chile, Chile

Email:
jkiwi@puc.cl

**John Milnor**

Affiliation:
Institute for Mathematical Sciences, Stony Brook University, Stony Brook, New York 11794-3660

Email:
jack@math.sunysb.edu

DOI:
https://doi.org/10.1090/S1088-4173-10-00204-3

Received by editor(s):
September 3, 2009

Published electronically:
March 9, 2010

Additional Notes:
The first author was partially supported by the Simons Foundation

The second author was supported by Research Network on Low Dimensional Dynamics PBCT/CONICYT, Chile

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.