Hiroki SUMI

Associate Professor
Department of Mathematics, Graduate School of Science, Osaka University
1-1 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan
office : Science Building B-516.
E-mail address: math.sci.osaka-u.ac.jp after sumi@

Updated on: January 30, 2012

[To pages in Japanese] [To homepage of Department of Mathematics, Osaka University]

Researches: Complex dynamical systems, random complex dynamical systems, fractal geometry.

Preprints

  1. H. Sumi and M. Urbanski, Transversality family of expanding rational semigroups, preprint, 36 pages, 3 figures. pdf file, ps file.
  2. H. Sumi, Random complex dynamics and devil's coliseums, preprint, 24 pages, 5 figures. pdf file, ps file.
  3. H. Sumi, Cooperation principle, stability and bifurcation in random complex dynamics, preprint, 38 pages, 5 figures. pdf file, ps file.
  4. H. Sumi, Dynamics of postcritically bounded polynomial semigroups II: fiberwise dynamics and the Julia sets, preprint, 22 pages, 1 figure. pdf file, ps file.
  5. H. Sumi and M. Urbanski, Bowen Parameter and Hausdorff Dimension for Expanding Rational Semigroups, preprint 2009, 17 pages, 2 figures. To appear in Discrete and Continuous Dynamical Systems Ser. A. pdf-file, ps-file.
  6. H. Sumi: Dynamics of postcritically bounded polynomial semigroups, preprint 2007, http://arxiv.org/abs/math/0703591. November 26, 2007 version. Lemma 4.31 and Lemma 4.37 are updated. This paper is a ``permanent preprint.'' ps-file, pdf file.

Publications

  1. R. Stankewitz and H. Sumi, Dynamical properties and structure of Julia sets of postcritically bounded polynomial semigroups, Trans. Amer. Math. Soc., 363 (2011), no. 10, 5293--5319. ps-file, pdf-file.
  2. H. Sumi and M. Urbanski, Measures and dimensions of Julia sets of semi-hyperbolic rational semigroups, Discrete and Continuous Dynamical Systems Ser. A., Vol. 30, No. 1, 2011, 313--363. 50 pages, 2 figures. pdf-file, ps-file.
  3. H. Sumi, Rational semigroups, random complex dynamics and singular functions on the complex plane, Selected Papers on Analysis and Differential Equations, Amer. Math. Soc. Transl. (2) Vol. 230, 2010, 161--200.
  4. H. Sumi, Random complex dynamics and semigroups of holomorphic maps, published in Proc. London. Math. Soc. (2011), 102 (1), 50--112. 56 pages, 5 figures. Revised on May 15, 2010. pdf-file, ps-file.
  5. H. Sumi, Dynamics of postcritically bounded polynomial semigroups I: connected components of the Julia sets, published in Discrete and Continuous Dynamical Systems Series A, Vol. 29, No. 3, 2011, 1205--1244. 39 pages, 2 figures. pdf-file, ps-file.
  6. H. Sumi, Dynamics of postcritically bounded polynomial semigroups III: classification of semi-hyperbolic semigroups and random Julia sets which are Jordan curves but not quasicircles, published in Ergodic Theory Dynam. Systems (2010), {\bf 30}, No. 6, 1869--1902. 29 pages, 1 figure. pdf-file, ps-file.
  7. H. Sumi and M. Urbanski, Real analyticity of Hausdorff dimension for expanding rational semigroups, published in Ergodic Theory Dynam. Systems (2010), Vol. 30, No. 2, 601-633. ps-file, pdf-file.
  8. H. Sumi, Interaction cohomology of forward or backward self-similar systems, 47 pages, 9 figures. Adv. Math., 222 (2009), no. 3, 729--781. ps-file, pdf-file.
  9. M. Roy, H. Sumi and M. Urbanski, Lambda-tolology VS. pointwise topology, Ergodic Theory Dynam. Systems 29 (2009), no. 2, 685-713. ps-file, pdf-file, dvi-file.
  10. H. Sumi and M. Urbanski, The equilibrium states for semigroups of rational maps, Monatsh. Math., 156 (2009), no. 4, 371--390. ps-file, pdf-file, dvi-file.
  11. H. Sumi, Rational semigroups, random complex dynamics and singular functions on the complex plane, ``Sugaku'' Vol. 61, No. 2, p133-161. Survey article, written in Japanese. (Note: `` Sugaku'' is a journal which is published by Mathematical Society of Japan. English version of this article will be published in ``Sugaku Exposition'' by the AMS.) [Correction: (I) p 138, line 4: remove ``cs.'' from the HP address. (II) Definition 50 (5) add ``$\tilde{J}(f)\neq \emptyset $ and '' in the beginning of the sentence.] In the following files of this homepage, the above matters are corrected. ps-file, pdf-file.
  12. M. Roy, H. Sumi and M. Urbanski, Analytic families of holomorphic iterated function systems, Nonlinearity 21 (2008) 2255-2279. ps-file, pdf-file, dvi-file.
  13. H. Sumi: Erratum to `Semi-hyperbolic fibered rational maps and rational semigroups' (Ergodic Theory and Dynamical Systems 26 (2006), 893-922), Ergodic Theory Dynam. Systems (2008) 28, 1043-1045. ps-file, pdf-file, dvi-file.
  14. H. Sumi, Random dynamics of polynomials and devil's-staircase-like functions in the complex plane, Appl. Math. Comput. 187 (2007), no. 1, 489--500. (Proceedings paper of a conference.)
  15. R. Stankewitz and H. Sumi, Structure of Julia sets of polynomial semigroups with bounded finite postcritical set, Appl. Math. Comput. 187 (2007), no. 1, 479--488. (Proceedings paper of a conference.)
  16. H. Sumi: Semi-hyperbolic fibered rational maps and rational semigroups Ergodic Theory Dynam. Systems. (2006), {\bf 26}, 893-922. (Revised on June 10, 2006. A typo in Theorem 2.6 is fixed.) ps-file, dvi-file, pdf-file
  17. H. Sumi: Dimensions of Julia sets of expanding rational semigroups, Kodai Mathematical Journal (2005), Vol. 28, No. 2, pp 390-422. ps-file, dvi-file, pdf-file
  18. R. Stankewitz, T. Sugawa and H. Sumi: Some counterexamples in dynamics of rational semigroups, Annales Academia Scientiarum Fennica Mathematica, Vol. 29, 2004, 357-366. ps-file, dvi-file, pdf-file.
  19. H. Sumi: Dynamics of sub-hyperbolic and semi-hyperbolic rational semigroups and skew products, Ergodic Theory Dynam. Systems (2001),{\bf 21}, 563-603
  20. H. Sumi: A correction to the proof of a lemma in `Dynamics of sub-hyperbolic and semi-hyperbolic rational semigroups and skew products', Ergodic Theory Dynam. Systems (2001),{\bf 21}, 1275-1276.
  21. H. Sumi: Skew product maps related to finitely generated rational semigroups, Nonlinearity, {\bf 13} (2000),995-1019.
  22. H. Kriete and H. Sumi: Semihyperbolic transcendental semigroups, J.Math.Kyoto.Univ.,Vol.40, No.2,(2000),205-216. pdf-file.
  23. H. Kriete and H. Sumi: Correction to ``Semihyperbolic transcendental semigroups'', J.Math.Kyoto.Univ.,Vol.45, No.2, (2005), 427.
  24. H. Sumi: On Hausdorff dimension of Julia sets of hyperbolic rational semigroups, Kodai. Math. J., Vol.21,No.1,(1998),10-28. pdf-file.
  25. H.Sumi: On dynamics of hyperbolic rational semigroups, J.Math.Kyoto.Univ. Vol.37, No.4, (1997), 717-733. pdf-file.

Presentation files

  1. Random complex dynamics and singular functions on the complex plane, at the conference ``Dynamical Systems II'' at University of North Texas, May 18 2009, and at the conference ``Advances in Low Dimensional Dynamics'' at Stony Brook University, June 8 2009. pdf-file.

Curriculum Vitae

  1. 1970 Born in Otsu, Japan
  2. 1994 Bachelor degree in Faculty of Science, Kyoto University (majoring mathematics)
  3. 1999 Ph. D. in Graduate School of Human and Environmental Studies, Kyoto University.
  4. 1999-2005 Assistant Professor in Department of Mathematics, Tokyo Institute of Technology
  5. 2005-- Associate Professor in Department of Mathematics, Graduate School of Science, Osaka University
  6. 2000 The MSJ Takebe Katahiro Prize for Encouragement of Young Researchers (from The Mathematical Society of Japan) [home page of Takebe Prize]

Links

  1. [ Complex Dynamics Conference of Academic Year 2011-2012 (January 23--January 27, 2012)]
  2. [ 2010 Complex dynamics conference ``Reseach on Complex Dynamics and Related Fields'' (celebrating Prof. Ushiki's 60th birthday) (December 6, 2010 -- December 10, 2010) homepage Japanese]
  3. [ 2009 Complex dynamics conference ``Integrated Research of Complex Dynamics and Related Fields'' (December 14, 2009 -- December 18, 2009) homepage]
  4. [ Rich Stankewitz home page]
  5. [ Home page of wonderful computer program to draw graphics of Julia sets and attractors of rational semigroups (semigroups of rational maps) by Rich Stankewitz and his students]
  6. [ Dr. Johannes Jaerisch (Post. Doc. Fellow of Osaka Univ.) ]