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Deformation of Brody curves and mean dimension

Published online by Cambridge University Press:  03 February 2009

MASAKI TSUKAMOTO
MASAKI TSUKAMOTO*
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan (email: tukamoto@math.kyoto-u.ac.jp)
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Abstract

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The main purpose of this paper is to show that ideas of deformation theory can be applied to ‘infinite-dimensional geometry’. We develop the deformation theory of Brody curves. A Brody curve is a kind of holomorphic map from the complex plane to the projective space. Since the complex plane is not compact, the parameter space of the deformation can be infinite-dimensional. As an application we prove a lower bound on the mean dimension of the space of Brody curves.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 5 , October 2009 , pp. 1641 - 1657
Copyright
Copyright © Cambridge University Press 2009

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