# 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.
In 2017 April, I move to Graduate School of Human and Environmental Studies, Kyoto University, to be a full professor there.
[To Graduate School of Human and Environmental Studies, Kyoto University]

Updated on: March 29, 2017.

### Preprints

1. R. Stankewitz, T. Sugawa and H. Sumi, Hereditarily Non Uniformly Perfect Sets, to appear in Discrete and Continuous Dynamical Systems Ser. A, 15 pages, pdf file.
2. H. Sumi, Negativity of Lyapunov Exponents and Convergence of Generic Random Polynomial Dynamical Systems and Random Relaxed Newton's Methods, 60 pages, pdf file.
3. J. Jaerisch and H. Sumi, Pointwise Hoelder exponents of the complex analogues of the Takagi function in random complex dynamics, provisionally accepted for publication in Adv. Math. pdf file.
4. J. Jaerisch and H. Sumi, Dynamics of infinitely generated nicely expanding rational semigroups and the inducing method, to appear in Trans. Amer. Math. Soc., 35 pages. pdf file.
5. 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. H. Sumi: On dynamics of hyperbolic rational semigroups, J. Math. Kyoto. Univ. Vol. 37, No. 4, (1997), 717-733. pdf-file.
2. H. Sumi: On Hausdorff dimension of Julia sets of hyperbolic rational semigroups, Kodai. Math. J., Vol.21,No.1,(1998),10-28. pdf-file.
3. H. Kriete and H. Sumi: Semihyperbolic transcendental semigroups, J. Math. Kyoto. Univ., Vol. 40, No.2,(2000),205-216. pdf-file.
4. H. Kriete and H. Sumi: Correction to Semihyperbolic transcendental semigroups'', J. Math. Kyoto. Univ., Vol. 45, No. 2, (2005), 427.
5. H. Sumi: Skew product maps related to finitely generated rational semigroups, Nonlinearity, 13 (2000), 995-1019.
6. H. Sumi: Dynamics of sub-hyperbolic and semi-hyperbolic rational semigroups and skew products, Ergodic Theory Dynam. Systems (2001), 21, 563-603
7. 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), 21, 1275-1276.
8. 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.
9. H. Sumi: Dimensions of Julia sets of expanding rational semigroups, Kodai mathematical Journal Vol.28, 2005, No.2, pp. 390-422. ps-file, dvi-file, pdf-file
10. H. Sumi: Semi-hyperbolic fibered rational maps and rational semigroups, Ergodic Theory Dynam. Systems (2006), 26, 893-922. (Revised on June 10, 2006. A typo in Theorem 2.6 is fixed.) ps-file, dvi-file, pdf-file.
11. 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.
12. 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.)
13. 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.)
14. 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.
15. 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 has been published in Selected papers on analysis and differential equations, 161-200, Amer. Math. Soc. Transl. Ser. 2, 230, Amer. Math. Soc., Providence, RI, 2010.'') [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.
16. 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.
17. 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.
18. 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.
19. 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.
20. 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), 30, No. 6, 1869--1902. 29 pages, 1 figure. pdf-file, ps-file.
21. 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.
22. 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.
23. 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.
24. 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.
25. 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.
26. H. Sumi and M. Urbanski, Bowen Parameter and Hausdorff Dimension for Expanding Rational Semigroups, Discrete and Continuous Dynamical Systems Ser. A, 32 (2012), no. 7, 2591--2606. pdf-file, ps-file.
27. H. Sumi and M. Urbanski, Transversality family of expanding rational semigroups, Advances in Mathematics 234 (2013) 697--734. pdf file, ps file.
28. H. Sumi, Cooperation principle, stability and bifurcation in random complex dynamics, 40 pages, 6 figures. Advances in Mathematics 245 (2013) 137--181. pdf file, ps file.
29. H. Sumi, Dynamics of postcritically bounded polynomial semigroups II: fiberwise dynamics and the Julia sets, 24 pages, 1 figure. J. London Math. Soc. (2) 88 (2013) 294--318. pdf file, ps file.
30. R. Stankewitz and H. Sumi, Random Backward Iteration Algorithm for Julia sets of Rational Semigroups, Discrete and Continuous Dynamical Systems Ser. A, 35 (2015), no. 5, 2165--2175. pdf file.
31. H. Sumi, Random complex dynamics and devil's coliseums, Nonlinearity 28 (2015) 1135-1161. pdf file.
32. J. Jaerisch and H. Sumi, Multifractal formalism for expanding rational semigroups and random complex dynamical systems, Nonlinearity 28 (2015) 2913-2938. pdf file.
33. H. Sumi, The space of 2-generator postcritically bounded polynomial semigroups and random complex dynamics, Adv. Math. 290 (2016) 809--859. pdf file.
34. R. Stankewitz and H Sumi, Backward Iteration Algorithms for Julia sets of Mobius Semigroups, Discrete and Continuous Dynamical Systems Ser. A, 36 (2016), 6475 - 6485. 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]
7. 2012 Osaka University President Award for Encourgement (for research)