Pólya enumeration theorem: Difference between revisions

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[[File:Mitsuhiro Shishikura.jpg|thumb|220px|{{PAGENAME}}]]
{{nihongo|'''Mitsuhiro Shishikura'''|宍倉 光広|Shishikura Mitsuhiro|born November 27, 1960}} is a [[Japan]]ese [[mathematician]] working in the field of [[complex dynamics]]. He is professor at [[Kyoto University]] in Japan.
 
Shishikura became internationally recognized<ref>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.</ref> for two of his earliest contributions, both of which solved long-standing [[open problems]].
* In his Master's thesis, he proved a conjectured of [[Pierre Fatou|Fatou]] from 1920<ref>P. Fatou, ''Sur les &eacute;quations fonctionelles'', Bull. Soc. Math. Fr., 1920</ref> by showing that a [[rational function]] of degree <math>d\,</math> has at most <math>2d-2\,</math> nonrepelling [[periodic cycle]]s.<ref>M. Shishikura, ''On the quasiconformal surgery of rational functions,'' Ann. Sci. École Norm. Sup. (4) 20 (1987), no. 1, 1–29.</ref>
* He proved<ref>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 ([http://arxiv.org/pdf/math/9201282v1.pdf preprint])</ref>  that the boundary of the [[Mandelbrot set]] has [[Hausdorff dimension]] two, confirming a conjecture stated by [[Benoit Mandelbrot|Mandelbrot]]<ref>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</ref> and [[John Milnor|Milnor]].<ref>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</ref>
 
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<ref>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</ref>)'' the existence of a [[entire function|transcendental entire function]] with a [[doubly connected]] [[wandering domain]], answering a question of Baker from 1985;<ref>I. N. Baker, ''Some entire functions with multiply-connected wandering domains'', Ergodic Theory Dynam. Systems 5 (1985), 163-169</ref>
* ''(in joint work with Inou<ref>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/</ref>)'' a study of ''near-parabolic renormalization'' which is essential in Buff and Chéritat's recent proof of the existence of polynomial [[Julia set]]s of positive planar [[Lebesgue measure]].
 
One of the main tools pioneered by Shishikura and used throughout his work is that of [[quasiconformal mapping|quasiconformal]] surgery.
 
==References==
{{Reflist}}
 
==External links==
*[http://www.math.kyoto-u.ac.jp/~mitsu/ Faculty home page] at Kyōto University
 
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
|name= Shishikura, Mitsuhiro
|alternative names=
|short description= Japanese mathematician
|date of birth=
|place of birth=
|date of death=
|place of death=
}}
 
{{DEFAULTSORT:Shishikura, Mitsuhiro}}
[[Category:1960 births]]
[[Category:Living people]]
[[Category:Japanese mathematicians]]
[[Category:Tokyo Institute of Technology faculty]]
[[Category:University of Tokyo faculty]]
[[Category:Kyoto University faculty]]
[[Category:Kyoto University alumni]]
[[Category:20th-century mathematicians]]
[[Category:21st-century mathematicians]]

Revision as of 17:54, 19 September 2013

Pólya enumeration theorem

Template:Nihongo 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.

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

One of the main tools pioneered by Shishikura and used throughout his work is that of quasiconformal surgery.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

Template:Persondata

  1. ↑ 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.
  2. ↑ P. Fatou, Sur les équations fonctionelles, Bull. Soc. Math. Fr., 1920
  3. ↑ M. Shishikura, On the quasiconformal surgery of rational functions, Ann. Sci. École Norm. Sup. (4) 20 (1987), no. 1, 1–29.
  4. ↑ 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)
  5. ↑ 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
  6. ↑ 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
  7. ↑ 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
  8. ↑ I. N. Baker, Some entire functions with multiply-connected wandering domains, Ergodic Theory Dynam. Systems 5 (1985), 163-169
  9. ↑ 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/
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