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is a Japanese mathematician working in the field of complex dynamics. He is professor at Kyoto University in Japan. Shishikura became internationally recognized〔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.〕 for two of his earliest contributions, both of which solved long-standing open problems. * In his Master's thesis, he proved a conjectured of Fatou from 1920〔P. Fatou, ''Sur les équations fonctionelles'', Bull. Soc. Math. Fr., 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〔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 ))〕 that the boundary of the Mandelbrot set has Hausdorff dimension two, confirming a conjecture stated by Mandelbrot〔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〕 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 Kisaka〔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〕)'' 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 Inou〔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/〕)'' 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. One of the main tools pioneered by Shishikura and used throughout his work is that of quasiconformal surgery. ==References== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Mitsuhiro Shishikura」の詳細全文を読む スポンサード リンク
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