Mitsuhiro Shishikura (Japanese: 宍倉 光広 Shishikura Mitsuhiro) is a Japanese mathematician working in the field of complex dynamics. He is currently professor at Kyoto University in Japan.

Shishikura became famous for two of his earliest contributions, both of which solved long-standing open problems.

• He improved on a result of Fatou by showing that a rational function of degree $d\backslash ,$ has at most $2d-2\backslash ,$ nonrepelling periodic cycles.
• He proved that the boundary of the Mandelbrot set has Hausdorff dimension two.

More recent results of Shishikura include

• (in joint work with Kisaka) the existence of a transcendental entire function with a doubly connected wandering domain;
• (in joint work with Inou) a study of near-parabolic renormalization which is essential in Buff and Chéritat's recent proof of the existence of Julia sets of positive planar Lebesgue measure.

One of the main tools pioneered by Shishikura and used throughout his work is that of quasiconformal surgery.

External links

• Faculty home page at Kyōto University

year of birth missing | living people | Japanese mathematicians | 宍倉光広