## Brody curves and mean dimension

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- by Shinichiroh Matsuo and Masaki Tsukamoto;
- J. Amer. Math. Soc.
**28**(2015), 159-182 - DOI: https://doi.org/10.1090/S0894-0347-2014-00798-0
- Published electronically: May 22, 2014
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## 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.## References

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## Bibliographic 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