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Geometry Colloquium
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Date, time & place | Friday 10:00 - 11:30 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2015/04/17
10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Masaki TSUKAMOTO (Kyoto University)
Mean dimension of the dynamical system of Brody curves (日本語)
Masaki TSUKAMOTO (Kyoto University)
Mean dimension of the dynamical system of Brody curves (日本語)
[ Abstract ]
Mean dimension is a topological invariant of dynamical systems with infinite dimension and infinite entropy. Brody curves are Lipschitz entire holomorphic curves, 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. A key novel ingredient is an information theoretic approach to mean dimension introduced by Lindenstrauss and Weiss.
Mean dimension is a topological invariant of dynamical systems with infinite dimension and infinite entropy. Brody curves are Lipschitz entire holomorphic curves, 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. A key novel ingredient is an information theoretic approach to mean dimension introduced by Lindenstrauss and Weiss.
