is a Japanese mathematician working in the field of complex dynamics. He is professor at Kyoto University in Japan.
Shishikura became internationally recognizedThis 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. for two of his earliest contributions, both of which solved long-standing open problems. In his Master's thesis, he proved a conjecture of Fatou from 1920 by showing that a rational function of degree has at most nonrepelling periodic cycles.M. Shishikura, On the quasiconformal surgery of rational functions, Ann. Sci. École Norm. Sup. (4) 20 (1987), no. 1, 1–29. He proved that the boundary of the Mandelbrot set has Hausdorff dimension two, confirming a conjecture stated by MandelbrotB. 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 and Milnor.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
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 (in joint work with KisakaM. 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) the existence of a transcendental entire function with a doubly connected wandering domain, answering a question of Baker from 1985;I. N. Baker, Some entire functions with multiply-connected wandering domains, Ergodic Theory Dynam. Systems 5 (1985), 163-169 (in joint work with InouH. Inou and M. Shishikura, The renormalization of parabolic fixed points and their perturbation, preprint, 2008, http://www.math.kyoto-u.ac.jp/~mitsu/pararenorm/) a study of near-parabolic renormalization which is essential in Buff and Chéritat's recent proof of the existence of polynomial Julia sets of positive planar Lebesgue measure. (in joint work with Cheraghi) A proof of the local connectivity of the Mandelbrot set at some infinitely satellite renormalizable points. (in joint work with Yang) A proof of the regularity of the boundaries of the high type Siegel disks of quadratic polynomials.
One of the main tools pioneered by Shishikura and used throughout his work is that of quasiconformal surgery.
His doctoral students include Weixiao Shen.
References
External links Faculty home page at Kyōto University