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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Errata for “Cubic polynomial maps with periodic critical orbit, Part II: Escape regions”
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by Araceli Bonifant, Jan Kiwi and John Milnor PDF
Conform. Geom. Dyn. 14 (2010), 190-193 Request permission

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 $\mathcal {E}_h$.
References
  • 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.
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2670510