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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Orbit portraits of unicritical antiholomorphic polynomials
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by Sabyasachi Mukherjee
Conform. Geom. Dyn. 19 (2015), 35-50
Published electronically: March 3, 2015


Orbit portraits were introduced by Goldberg and Milnor as a combinatorial tool to describe the patterns of all periodic dynamical rays landing on a periodic cycle of a quadratic polynomial. This encodes information about the dynamics and the parameter spaces of these maps. We carry out a similar analysis for unicritical antiholomorphic polynomials, and give an explicit description of the orbit portraits that can occur for such maps in terms of their characteristic angles, which turns out to be rather restricted when compared with the holomorphic case. Finally, we prove a realization theorem for these combinatorial objects. The results obtained in this paper serve as a combinatorial foundation for a detailed understanding of the combinatorics and topology of the parameter spaces of unicritical antiholomorphic polynomials and their connectedness loci, known as the multicorns.
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Bibliographic Information
  • Sabyasachi Mukherjee
  • Affiliation: Jacobs University Bremen, Campus Ring 1, Bremen 28759, Germany
  • MR Author ID: 1098266
  • ORCID: 0000-0002-6868-6761
  • Email:
  • Received by editor(s): June 15, 2014
  • Received by editor(s) in revised form: February 1, 2015, and February 2, 2015
  • Published electronically: March 3, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 19 (2015), 35-50
  • MSC (2010): Primary 37E15, 37E10, 37F10, 37F20
  • DOI:
  • MathSciNet review: 3317234