# Mitsuhiro Shishikura

Mitsuhiro Shishikura

Mitsuhiro Shishikura (宍倉 光広 Shishikura Mitsuhiro, born November 27, 1960) is a Japanese mathematician working in the field of complex dynamics. He is professor at Kyoto University in Japan.

Shishikura became internationally recognized[1] for two of his earliest contributions, both of which solved long-standing open problems.

For his results, he was awarded the Salem Prize in 1992, and the Iyanaga Spring Prize of the Mathematical Society of Japan in 1995.

More recent results of Shishikura include

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

## References

1. ^ This recognition is evidenced e.g. by the prizes he received (see below) as well as his invitation as an invited speaker in the Real & Complex Analysis Section of the 1994 International Congress of Mathematicians; see http://www.mathunion.org/o/ICM/Speakers/SortedByCongress.php.
2. ^ P. Fatou, Sur les équations fonctionelles, Bull. Soc. Math. Fr., 1920
3. ^ M. Shishikura, On the quasiconformal surgery of rational functions, Ann. Sci. École Norm. Sup. (4) 20 (1987), no. 1, 1–29.
4. ^ M. Shishikura, The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets, Ann. of Math. (2) 147 (1998), no. 2, 225–267 (preprint)
5. ^ B. Mandelbrot, On the dynamics of iterated maps V: Conjecture that the boundary of the M-set has a fractal dimension equal to 2, in: Chaos, Fractals and Dynamics, Eds. Fischer and Smith, Marcel Dekker, 1985, 235-238
6. ^ J. Milnor, Self-similarity and hairiness in the Mandelbrot set, in: Computers in Geometry and Topology, ed. M. C. Tangora, Lect. Notes in Pure and Appl. Math., Marcel Dekker, Vol. 114 (1989), 211-257
7. ^ M. Kisaka and 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
8. ^ I. N. Baker, Some entire functions with multiply-connected wandering domains, Ergodic Theory Dynam. Systems 5 (1985), 163-169
9. ^ H. Inou and M. Shishikura, The renormalization of parabolic fixed points and their perturbation, preprint, 2008, http://www.math.kyoto-u.ac.jp/~mitsu/pararenorm/
10. ^ D. Cheraghi and M. Shishikura, Satellite renormalization of quadratic polynomials, preprint, 2015, https://arxiv.org/abs/1509.07843
11. ^ M. Shishikura and F. Yang, The high type quadratic Siegel disks are Jordan domains, preprint, 2016, https://arxiv.org/abs/1608.04106