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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Brody curves and mean dimension
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by Shinichiroh Matsuo and Masaki Tsukamoto PDF
J. Amer. Math. Soc. 28 (2015), 159-182 Request permission

Abstract:

We study the mean dimensions of the systems of Brody curves. In particular we give the formula of the mean dimension of the system of Brody curves in the Riemann sphere. A key notion is a non-degeneracy of Brody curves introduced by Yosida (1934). We develop a deformation theory of non-degenerate Brody curves and apply it to the calculation of the mean dimension. Moreover we show that there are sufficiently many non-degenerate Brody curves by using the method of gluing infinitely many rational curves.
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Additional Information
  • Shinichiroh Matsuo
  • Affiliation: Department of Mathematics, Osaka University, Toyonaka, Osaka 560-0043, Japan
  • Email: matsuo@math.sci.osaka-u.ac.jp
  • Masaki Tsukamoto
  • Affiliation: Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
  • MR Author ID: 828585
  • Email: tukamoto@math.kyoto-u.ac.jp
  • Received by editor(s): June 28, 2012
  • Received by editor(s) in revised form: January 6, 2014
  • Published electronically: May 22, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 28 (2015), 159-182
  • MSC (2010): Primary 32H30, 54H20
  • DOI: https://doi.org/10.1090/S0894-0347-2014-00798-0
  • MathSciNet review: 3264765