Mean dimension of the dynamical system of Brody curves

研究成果: Contribution to journalArticle

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抜粋

Mean dimension is a topological invariant of dynamical systems counting the number of parameters averaged by dynamics. Brody curves are Lipschitz holomorphic maps f: C→ CPN, and they form an infinite dimensional dynamical system. Gromov started the problem of estimating its mean dimension in 1999. We solve this problem by proving the exact mean dimension formula. Our formula expresses the mean dimension by the energy density of Brody curves. As a key novel ingredient, we use an information theoretic approach to mean dimension introduced by Lindenstrauss and Weiss.

元の言語英語
ページ(範囲)935-968
ページ数34
ジャーナルInventiones Mathematicae
211
発行部数3
DOI
出版物ステータス出版済み - 3 1 2018
外部発表Yes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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