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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Normality and repelling periodic points
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by Jianming Chang and Lawrence Zalcman PDF
Trans. Amer. Math. Soc. 363 (2011), 5721-5744 Request permission

Abstract:

Let $k\geq 3(\geq 2)$ be an integer and $\mathcal {F}$ be a family of functions meromorphic in a domain $D\subset \mathbb {C}$, all of whose poles have multiplicity at least 2 (at least 3). If in $D$ each $f\in \mathcal {F}$ has neither repelling fixed points nor repelling periodic points of period $k$, then $\mathcal {F}$ is a normal family in $D$. Examples are given to show that the conditions on poles are necessary and sharp.
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Additional Information
  • Jianming Chang
  • Affiliation: Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, People’s Republic of China
  • Email: jmchang@cslg.edu.cn
  • Lawrence Zalcman
  • Affiliation: Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel
  • Email: zalcman@macs.biu.ac.il
  • Received by editor(s): September 6, 2009
  • Published electronically: June 17, 2011
  • Additional Notes: The research of the first author was supported by NNSF of China (Grant No. 10871094), NSFU of Jiangsu, China (Grant No. 08KJB110001), Qinglan Project of Jiangsu, China, and the SRF for ROCS, SEM.
    The research of the second author was supported by Israel Science Foundation Grant 395/07. This work is part of the European Science Foundation Networking Programme HCAA.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 5721-5744
  • MSC (2000): Primary 30D45, 30D05, 37F10, 37C25
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05280-3
  • MathSciNet review: 2817406