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 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 His doctoral students include Weixiao Shen.
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| - Mitsuhiro Shishikura (de)
- Mitsuhiro Shishikura (en)
- 宍倉光広 (ja)
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| - 宍倉 光広（ししくら みつひろ、1960年11月27日 - ）は日本の数学者。京都大学教授。専門は、力学系理論。 1983年に京都大学理学部を卒業。1988年に同大学院理学研究科博士課程修了。プリンストン高等研究所所員、東京工業大学助手・助教授、東京大学助教授、広島大学教授を経て、現職。 力学系の中でもフラクタルの研究を活発に行っている。特に複素平面上のマンデルブロ集合についての研究は有名で、境界のハウスドルフ次元が2であるというマンデルブロの予想を証明した。 1992年にはサレム賞、1995年には日本数学会春季賞日本数学会彌永賞（1973年春-1987年春）を受賞した。 (ja)
- Mitsuhiro Shishikura (jap. 宍倉 光広, Shishikura Mitsuhiro; * 27. November 1960) ist ein japanischer Mathematiker, der sich mit Dynamischen Systemen und speziell komplexer Dynamik befasst. Er ist Professor an der Universität Kyōto. 1988 promovierte (Trees associated with the configuration of Herman rings) er an der Universität Kyoto. Shishikura bewies zwei wichtige, lange offene Probleme in der komplexen Dynamik: In seinen Arbeiten zur komplexen Dynamik führte er die Methode quasikonformer Chirurgie ein. (de)
- 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 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 His doctoral students include Weixiao Shen. (en)
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| - Mitsuhiro Shishikura (jap. 宍倉 光広, Shishikura Mitsuhiro; * 27. November 1960) ist ein japanischer Mathematiker, der sich mit Dynamischen Systemen und speziell komplexer Dynamik befasst. Er ist Professor an der Universität Kyōto. 1988 promovierte (Trees associated with the configuration of Herman rings) er an der Universität Kyoto. Shishikura bewies zwei wichtige, lange offene Probleme in der komplexen Dynamik:
* In seiner Diplomarbeit bewies er eine Vermutung von Pierre Fatou von 1920, dass eine rationale Funktion vom Grad bei Iteration höchstens nicht-abstoßende periodische Zyklen hat.
* 1998 bewies er eine Vermutung von Benoit Mandelbrot und John Milnor, dass die Hausdorff-Dimension des Rands einer Mandelbrot-Menge 2 ist. In seinen Arbeiten zur komplexen Dynamik führte er die Methode quasikonformer Chirurgie ein. 2008 bewies er die Existenz einer transzendentalen ganzen Funktion mit zweifach zusammenhängendem wanderndem Gebiet. Seine Arbeit mit H. Inoue von 2008 spielt eine Rolle im Beweis von Xavier Buff und Arnaud Chéritat über Julia-Mengen polynomialer Abbildungen mit positivem Lebesgue-Maß. 1995 erhielt er den Frühlingspreis der Japanischen Mathematischen Gesellschaft und 1992 den Salem-Preis. 1994 war er Invited Speaker auf dem Internationalen Mathematikerkongress in Zürich (Topological, Geometric and Complex Analytic Properties of Julia sets). (de)
- 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 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 by showing that a rational function of degree has at most nonrepelling .
* He proved that the boundary of the Mandelbrot set has Hausdorff dimension two, confirming a conjecture stated by Mandelbrot and Milnor. 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) the existence of a transcendental entire function with a doubly connected wandering domain, answering a question of Baker from 1985;
* (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 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. (en)
- 宍倉 光広（ししくら みつひろ、1960年11月27日 - ）は日本の数学者。京都大学教授。専門は、力学系理論。 1983年に京都大学理学部を卒業。1988年に同大学院理学研究科博士課程修了。プリンストン高等研究所所員、東京工業大学助手・助教授、東京大学助教授、広島大学教授を経て、現職。 力学系の中でもフラクタルの研究を活発に行っている。特に複素平面上のマンデルブロ集合についての研究は有名で、境界のハウスドルフ次元が2であるというマンデルブロの予想を証明した。 1992年にはサレム賞、1995年には日本数学会春季賞日本数学会彌永賞（1973年春-1987年春）を受賞した。 (ja)
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