KAMEYAMA Atsushi

KAMEYAMA Atsushi
Title Professor
Department Department of Electrical, Electronic and Computer Engineering
Course Applied Physics Course

Research fields

I am a mathematician in the area of dynamical systems, specifically, working on topological and combinatorial aspects of complex dynamics, low-dimensional dynamics, and fractals.

Julia sets are fractals which arise in the dynamics of rational functions on the Riemann sphere.
One of my goals is to clarify how the structure of the Julia sets reflects the combinatorial property of the dynamics of rational functions.

As well as rational functions, I study the dynamics of certain maps which are considered fundamental.
For example, power maps such as squaring or cubing are among the most fundamental maps.
A quasi-power map is defined as the composition of a power map and a rotation.
I investigate the dynamics of a family of quasi-power maps, which reveals a rich structure.

Combinatorics of fractals is also my interest.
Most of Fractals with well understood combinatorics are low-dimensional so far.
I explore the new type of high-dimensional fractals which have some good combinatorics.

The Levy curve fractal has a positive area.

Research Keywords

dynamicsl systems fractals Julia

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