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Errata for “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), 190-193
MSC (2010): Primary 37F10, 30C10, and, 30D05
DOI: https://doi.org/10.1090/S1088-4173-2010-00213-4
Published electronically: July 26, 2010
Original Article: Conform. Geom. Dyn. 14 (2010), 68-112.
MathSciNet review: 2670510
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Abstract: In this note we fill in some essential details which were missing from our paper. In the case of an escape region $\mathcal {E}_h$ with non-trivial kneading sequence, we prove that the canonical parameter $t$ can be expressed as a holomorphic function of the local parameter $\eta =a^{-1/\mu }$ (where $a$ is the periodic critical point). Furthermore, we prove that for any escape region $\mathcal {E}_h$ of grid period $n\ge 2$, the winding number $\nu$ of $\mathcal {E}_h$ over the $t$-plane is greater or equal than the multiplicity $\mu$ of $\mathcal {E}_h$.


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  • A. Bonifant, J. Kiwi and J. Milnor, Cubic Polynomial Maps with Periodic Critical Orbit, Part II: Escape Regions, Conformal Geometry and Dynamics 14 (2010) 68–112.

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Additional Information

Araceli Bonifant
Affiliation: Department of Mathematics, University of Rhode Island, 5 Lippitt Road, Room 200, Kingston, Rhode Island 02881
MR Author ID: 600241
Email: bonifant@math.uri.edu

Jan Kiwi
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica, Casilla 306, Correo 22, Santiago de Chile, Chile
Email: jkiwi@mat.puc.cl

John Milnor
Affiliation: Institute for Mathematical Sciences, Stony Brook University, Stony Brook, New York 11794-3660
MR Author ID: 125060
Email: jack@math.sunysb.edu

Received by editor(s): April 2, 2010
Published electronically: July 26, 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.