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.
(in joint work with Inou[9]) 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.[10]
(in joint work with Yang) A proof of the regularity of the boundaries of the high type
Siegel disks of quadratic polynomials.[11]
One of the main tools pioneered by Shishikura and used throughout his work is that of
quasiconformal surgery.
^M. Shishikura, On the quasiconformal surgery of rational functions, Ann. Sci. École Norm. Sup. (4) 20 (1987), no. 1, 1–29.
^Shishikura, Mitsuhiro (1998). "The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets". Annals of Mathematics. Second Series. 147 (2): 225–267.
arXiv:math/9201282.
doi:
10.2307/121009.
JSTOR121009.
MR1626737.
^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
^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
^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
^I. N. Baker, Some entire functions with multiply-connected wandering domains, Ergodic Theory Dynam. Systems 5 (1985), 163-169
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.
(in joint work with Inou[9]) 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.[10]
(in joint work with Yang) A proof of the regularity of the boundaries of the high type
Siegel disks of quadratic polynomials.[11]
One of the main tools pioneered by Shishikura and used throughout his work is that of
quasiconformal surgery.
^M. Shishikura, On the quasiconformal surgery of rational functions, Ann. Sci. École Norm. Sup. (4) 20 (1987), no. 1, 1–29.
^Shishikura, Mitsuhiro (1998). "The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets". Annals of Mathematics. Second Series. 147 (2): 225–267.
arXiv:math/9201282.
doi:
10.2307/121009.
JSTOR121009.
MR1626737.
^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
^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
^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
^I. N. Baker, Some entire functions with multiply-connected wandering domains, Ergodic Theory Dynam. Systems 5 (1985), 163-169