- Masaki TSUKAMOTO
- tsukamoto (please add
- Research Area
- dynamical systems, ergodic theory, mean dimension
My main subject is mean dimension of dynamical systems. Mean dimension is the number of parameters per unit time for describing dynamical systems. This was first introduced by Gromov in 1999. His main motivation is to propose a new approach to geometric analysis via mean dimension. Lindenstrauss and Weiss found several applications of mean dimension to classical problems in topological dynamics. I have been studying both Gromov's original approach and Lindenstrauss--Weiss' approach.
More concretely, I have been studying the following three subjects:
(1) Mean dimension of the dynamical systems of holomorphic curves.
(2) Problem of embedding dynamical systems into Hilbert cubes.
(3) Variational principles between mean dimension and rate distortion function in information theory.