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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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Nevanlinna theoretical exceptional sets of rational towers and semigroups
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by Yûsuke Okuyama PDF
Conform. Geom. Dyn. 10 (2006), 100-116 Request permission

Abstract:

For a rational tower, i.e., a composition sequence of rational maps, in addition to the algebraic and dynamical exceptional sets, various Nevanlinna theoretical exceptional sets are defined, and as we showed previously in the case of iterations, all of them are the same. In this paper, we extend this result to the cases of a rational tower with summable distortions and a finitely generated rational semigroup. We show that all the exceptional sets of a finitely generated rational semigroup are countable, and all of them are empty if and only if the algebraic one is as well (this being the smallest among them). The countability of exceptional sets is fundamental in the Nevanlinna theory, and their emptiness is important in the complex dynamics.
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Additional Information
  • Yûsuke Okuyama
  • Affiliation: Department of Mathematics, Faculty of Science, Kanazawa University, Kanazawa 920-1192 Japan
  • Address at time of publication: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68 (Gustaf Hällströmin katu 2b), FI-00014 Helsinki, Finland
  • Email: yusuke.okuyama@helsinki.fi
  • Received by editor(s): April 19, 2005
  • Received by editor(s) in revised form: October 13, 2005
  • Published electronically: April 6, 2006
  • Additional Notes: Partially supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan, Grant-in-Aid for Young Scientists (B), 15740085, 2004
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 10 (2006), 100-116
  • MSC (2000): Primary 30D35; Secondary 37F15, 32H50
  • DOI: https://doi.org/10.1090/S1088-4173-06-00140-8
  • MathSciNet review: 2218642