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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

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Cubic polynomial maps with periodic critical orbit, Part II: Escape regions
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by Araceli Bonifant, Jan Kiwi and John Milnor
Conform. Geom. Dyn. 14 (2010), 68-112
Published electronically: March 9, 2010

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


The parameter space $\mathcal {S}_p$ 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 $\mathcal {S}_p$ 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 $\mathcal {S}_p$, 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 $\mathcal {S}_p$.
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Bibliographic Information
  • Araceli Bonifant
  • Affiliation: Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881
  • MR Author ID: 600241
  • Email:
  • Jan Kiwi
  • Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica, Casilla 306, Correo 22, Santiago de Chile, Chile
  • Email:
  • John Milnor
  • Affiliation: Institute for Mathematical Sciences, Stony Brook University, Stony Brook, New York 11794-3660
  • MR Author ID: 125060
  • Email:
  • 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
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 14 (2010), 68-112
  • MSC (2010): Primary 37F10, 30C10, 30D05
  • DOI:
  • MathSciNet review: 2600536