is a Japanese

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

working in the field of

complex dynamics Complex dynamics is the study of dynamical systems defined by Iterated function, iteration of functions on complex number spaces. Complex analytic dynamics is the study of the dynamics of specifically analytic functions. Techniques *General **Mo ...

. He is professor at

Kyoto University , mottoeng = Freedom of academic culture , established = , type = National university, Public (National) , endowment = ¥ 316 billion (2.4 1000000000 (number), billion USD) , faculty = 3,480 (Teaching Staff) , administrative_staff ...

in Japan. Shishikura became internationally recognized for two of his earliest contributions, both of which solved long-standing

open problems In science and mathematics, an open problem or an open question is a known problem which can be accurately stated, and which is assumed to have an objective and verifiable solution, but which has not yet been solved (i.e., no solution for it is know ...

. * In his Master's thesis, he proved a conjectured of Fatou from 1920 by showing that a

rational function In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rat ...

of degree

d\,

has at most

2d-2\,

nonrepelling periodic cycles. * He proved that the boundary of the

Mandelbrot set The Mandelbrot set () is the set of complex numbers c for which the function f_c(z)=z^2+c does not diverge to infinity when iterated from z=0, i.e., for which the sequence f_c(0), f_c(f_c(0)), etc., remains bounded in absolute value. This ...

has

Hausdorff dimension In mathematics, Hausdorff dimension is a measure of ''roughness'', or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a ...

two, confirming a conjecture stated by Mandelbrot and

Milnor John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook Univ ...

. For his results, he was awarded the

Salem Prize The Salem Prize, in memory of Raphael Salem, is awarded each year to young researchers for outstanding contributions to the field of analysis. It is awarded by the School of Mathematics at the Institute for Advanced Study in Princeton and was fo ...

in 1992, and the Iyanaga Spring Prize of the

Mathematical Society of Japan The Mathematical Society of Japan (MSJ, ja, 日本数学会) is a learned society for mathematics in Japan. In 1877, the organization was established as the ''Tokyo Sugaku Kaisha'' and was the first academic society in Japan. It was re-organized ...

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 set In the context of complex dynamics, a branch of mathematics, the Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou set of the function consists of values wit ...

s of positive planar

Lebesgue measure In measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of ''n''-dimensional Euclidean space. For ''n'' = 1, 2, or 3, it coincides wit ...

. * ''(in joint work with Cheraghi) A proof of the local connectivity of the

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 In mathematical complex analysis, a quasiconformal mapping, introduced by and named by , is a homeomorphism between plane domains which to first order takes small circles to small ellipses of bounded eccentricity. Intuitively, let ''f'' : ''D ...

surgery. His doctoral students include Weixiao Shen.

References

External links

Faculty home page
at Kyōto University {{DEFAULTSORT:Shishikura, Mitsuhiro 1960 births Living people Tokyo Institute of Technology faculty University of Tokyo faculty Kyoto University faculty Kyoto University alumni 20th-century Japanese mathematicians 21st-century Japanese mathematicians