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Brody curves and mean dimension

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Brody curve is a 1-Lipschitz holomorphic map from the complex plane to the complex projective space. The space of Brody curves is infinite dimensional and admits a natural group action. So it becomes an infinite dimensional dynamical system. I will study this system from the view point of Gromov’s mean dimension theory. Our main result is the formula of the mean dimension of the system of Brody curves in the Riemann sphere. Our idea can be also applied to Anti-Self-Dual Yang—Mills equation. If I have an enough time, I will also discuss it. This talk is based on the joint works with Shinichiroh Matsuo.

This talk is part of the Discrete Analysis Seminar series.

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