Mitsuhiro Shishikura

Mitsuhiro Shishikura, Oberwolfach 2008

Mitsuhiro Shishikura ( Japanese 宍倉光広 , Shishikura Mitsuhiro ; born November 27, 1960 ) is a Japanese mathematician who deals with dynamic systems and especially complex dynamics. He is a professor at Kyoto University .

In 1988 he received his doctorate ( Trees associated with the configuration of Herman rings ) from Kyoto University.

Shishikura proved two important, long open problems in the complex dynamics:

In his diploma thesis he proved a conjecture by Pierre Fatou from 1920 that a rational function of the degree at iteration has at most non-repulsive periodic cycles. ${\ displaystyle d}$ ${\ displaystyle 2d-2}$
In 1998 he proved a conjecture by Benoit Mandelbrot and John Milnor that the Hausdorff dimension of the edge of a Mandelbrot set is 2.

In his work on complex dynamics, he introduced the method of quasi-conformal surgery.

In 2008 he proved the existence of a transcendental whole function with doubly connected wandering area. His work with H. Inoue from 2008 plays a role in the proof of Xavier Buff and Arnaud Chéritat about Julia sets of polynomial maps with positive Lebesgue measure .

In 1995 he received the Spring Prize of the Japanese Mathematical Society and in 1992 the Salem Prize . In 1994 he was invited speaker at the International Congress of Mathematicians in Zurich ( Topological, Geometric and Complex Analytic Properties of Julia sets ).

Web links

Homepage
Mitsuhiro Shishikura in the Mathematics Genealogy Project (English)

Individual evidence

↑ Entry 000000200102 in the Doctoral Dissertation Bibliographic Database of the National Institute of Informatics
↑ Shishikura: On the quasiconformal surgery of rational functions , Ann. Sci. École Norm. Sup. (4) 20 (1987) no. 1, 1-29
↑ Shishikura: The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets , Ann. of Math. (2) 147 (1998) no. 2, 225-267
↑ M. Kisaka, M. Shishikura: On multiply connected wandering domains of entire functions , in: Transcendental dynamics and complex analysis, London Math. Soc. Lecture Note Ser., 348, Cambridge Univ. Press, Cambridge, 2008, 217-250
^ Inoue, Shishikura: The renormalization of parabolic fixed points and their perturbation , Preprint, 2008

personal data
SURNAME	Shishikura, Mitsuhiro
ALTERNATIVE NAMES	宍倉光広 (Japanese)
BRIEF DESCRIPTION	Japanese mathematician
DATE OF BIRTH	November 27, 1960

[1] Entry 000000200102 in the Doctoral Dissertation Bibliographic Database of the National Institute of Informatics

[2] Shishikura: On the quasiconformal surgery of rational functions , Ann. Sci. École Norm. Sup. (4) 20 (1987) no. 1, 1-29

[3] Shishikura: The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets , Ann. of Math. (2) 147 (1998) no. 2, 225-267

[4] M. Kisaka, M. Shishikura: On multiply connected wandering domains of entire functions , in: Transcendental dynamics and complex analysis, London Math. Soc. Lecture Note Ser., 348, Cambridge Univ. Press, Cambridge, 2008, 217-250

[5] Inoue, Shishikura: The renormalization of parabolic fixed points and their perturbation , Preprint, 2008