Hiroki SUMI
Professor
Division of Mathematical and Information Sciences
Department of Human and Environmental Studies
Graduate School of Human and Environmental Studies
Kyoto University
Address:
Yoshida Nihonmatsucho, Sakyoku, Kyoto, 6068501, Japan
office : Graduate School of Human and Environmental Studies Building 231.
Email address: math.h.kyotou.ac.jp after sumi@
[To
Department of Human Coexistence,
Graduate School of Human and Environmental Studies, Kyoto University]
Updated on: April 5, 2023.
[To pages in Japanese]
Researches: Holomorphic dynamical systems, Random holomorphic dynamical systems,
Iterated function systems, Fractal geometry, Complex Analysis, Ergodic Theory.
Preprints

K.Inui and H. Sumi,
Packing measure and dimension of the limit sets of IFSs of
generalized complex continued fractions,
preprint.
pdf file.
 M. Comerford, K. Falk, R. Stankewitz, H. Sumi, Hereditarily Non Uniformly Perfect Analytic and
Conformal Nonautonomous Attractor Sets, preprint, 14 pages,
pdf file.

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.''
psfile,
pdf file.
Publications

H. Sumi:
On dynamics of hyperbolic rational semigroups,
J. Math. Kyoto. Univ.
Vol. 37, No. 4, (1997), 717733.
pdffile.

H. Sumi: On Hausdorff dimension of Julia sets of hyperbolic
rational semigroups,
Kodai. Math. J.,
Vol.21,No.1,(1998),1028.
pdffile.

H. Kriete and H. Sumi:
Semihyperbolic transcendental semigroups,
J. Math. Kyoto. Univ., Vol. 40, No.2,(2000),205216.
pdffile.

H. Kriete and H. Sumi: Correction to ``Semihyperbolic transcendental semigroups'',
J. Math. Kyoto. Univ., Vol. 45, No. 2, (2005), 427.

H. Sumi:
Skew product maps related to finitely generated
rational semigroups,
Nonlinearity, 13 (2000), 9951019.

H. Sumi:
Dynamics of subhyperbolic and semihyperbolic
rational semigroups and skew products,
Ergodic Theory Dynam. Systems (2001), 21, 563603

H. Sumi:
A correction to the proof of a lemma in
`Dynamics of subhyperbolic and semihyperbolic
rational semigroups and skew products',
Ergodic Theory Dynam. Systems (2001), 21, 12751276.

R. Stankewitz, T. Sugawa and H. Sumi:
Some counterexamples in dynamics of rational semigroups,
Annales Academia Scientiarum Fennica Mathematica,
Vol. 29, 2004, 357366.
psfile,
dvifile,
pdffile.

H. Sumi: Dimensions of Julia sets of expanding rational semigroups,
Kodai mathematical Journal Vol.28, 2005, No.2, pp. 390422.
psfile,
dvifile,
pdffile

H. Sumi: Semihyperbolic fibered rational maps and rational semigroups,
Ergodic Theory Dynam. Systems (2006),
26, 893922. (Revised on June 10, 2006. A typo in Theorem 2.6 is fixed.)
psfile,
dvifile,
pdffile.

H. Sumi:
Erratum to `Semihyperbolic fibered rational maps and rational semigroups'
(Ergodic Theory and Dynamical Systems 26 (2006) 893922),
Ergodic Theory Dynam. Systems (2008), 28, 10431045.
psfile,
pdffile,
dvifile.
 R. Stankewitz and H. Sumi,
Structure of Julia sets of polynomial semigroups with bounded finite postcritical set,
Appl. Math. Comput. 187 (2007), no. 1, 479488. (Proceedings paper of a conference.)

H. Sumi,
Random dynamics of polynomials and devil'sstaircaselike functions in the complex plane,
Appl. Math. Comput. 187 (2007), no. 1, 489500. (Proceedings paper of a conference.)

M. Roy, H. Sumi and M. Urbanski,
Analytic families of holomorphic iterated function systems,
Nonlinearity 21 (2008) 22552279.
psfile,
pdffile,
dvifile.

H. Sumi, Rational semigroups, random complex dynamics and singular functions on the complex plane, ``Sugaku'' Vol. 61, No. 2, p133161. 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, 161200, 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.
psfile,
pdffile.

H. Sumi and M. Urbanski,
The equilibrium states for semigroups of rational maps,
Monatsh. Math., 156 (2009), no. 4, 371390.
psfile,
pdffile,
dvifile.

M. Roy, H. Sumi and M. Urbanski,
Lambdatolology VS. pointwise topology,
Ergodic Theory Dynam. Systems 29 (2009), no. 2, 685713.
psfile,
pdffile,
dvifile.

H. Sumi,
Interaction cohomology of forward or backward selfsimilar systems,
47 pages, 9 figures. Adv. Math., 222 (2009), no. 3, 729781.
psfile,
pdffile.

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, 601633.
psfile,
pdffile.
 H. Sumi, Dynamics of postcritically bounded polynomial semigroups III:
classification of semihyperbolic semigroups and
random Julia sets which are Jordan curves but not quasicircles,
published in Ergodic Theory Dynam. Systems (2010), 30, No. 6, 18691902. 29 pages, 1 figure.
pdffile,
psfile.

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, 12051244. 39 pages, 2 figures.
pdffile,
psfile.
 H. Sumi,
Random complex dynamics and semigroups of holomorphic maps,
published in Proc. London. Math. Soc. (2011), 102 (1), 50112.
56 pages, 5 figures. Revised on May 15, 2010.
pdffile,
psfile.
 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, 161200.

H. Sumi and M. Urbanski,
Measures and dimensions of Julia sets of semihyperbolic rational semigroups,
Discrete and Continuous Dynamical Systems Ser. A., Vol 30, No. 1, 2011, 313363.
50 pages, 2 figures.
pdffile,
psfile.

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, 52935319.
psfile,
pdffile.
 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, 25912606.
pdffile,
psfile.
 H. Sumi and M. Urbanski,
Transversality family of expanding rational semigroups,
Advances in Mathematics 234 (2013) 697734.
pdf file,
ps file.
 H. Sumi,
Cooperation principle, stability and bifurcation in random complex dynamics,
40 pages, 6 figures.
Advances in Mathematics 245 (2013) 137181.
pdf file,
ps file.
 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) 294318.
pdf file,
ps file.

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, 21652175.
pdf file.
 H. Sumi,
Random complex dynamics and devil's coliseums,
Nonlinearity 28 (2015) 11351161.
pdf file.
 J. Jaerisch and H. Sumi,
Multifractal formalism for expanding rational semigroups and random complex dynamical systems, Nonlinearity 28 (2015) 29132938.
pdf file.

H. Sumi,
The space of 2generator postcritically bounded polynomial semigroups
and random complex dynamics, Adv. Math. 290 (2016) 809859.
pdf file.
 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.
 J. Jaerisch and H. Sumi, Pointwise Hoelder exponents of the
complex analogues of the Takagi function in random complex dynamics,
Adv. Math. 313 (2017) 839874.
pdf file.
 J. Jaerisch and H. Sumi,
Dynamics of infinitely generated nicely expanding rational semigroups
and the inducing method,
Trans. Amer. Math. Soc. 369 (2017), no. 9, 61476187.
pdf file.
 R. Stankewitz, T. Sugawa and H. Sumi,
Hereditarily Non Uniformly Perfect Sets,
Discrete and Continuous Dynamical Systems Ser. S,
12, no. 8, (2019), 23912402.
15 pages, pdf file.

H. Sumi and T. Watanabe,
Noni.i.d. random holomorphic dynamical systems and the probability of tending to infinity,
Nonlinearity, 32 (2019), 37423771.
pdf file.
 M.Comerford, R. Stankewitz, H. Sumi,
Hereditarily non Uniformly Perfect
nonAutonomous Julia Sets,
Discrete and Continuous Dynamical Systems Ser. A,
40 (2020), no. 1, 3346.
pdf file.

K. Inui, H. Okada and H. Sumi,
The Hausdorff dimension function of the family of conformal iterated function systems of generalized
complex continued fractions,
Discrete and Continuous Dynamical Systems Ser. A, 40 (2020), no. 2, 753766.
pdf file.

K. Inui and H. Sumi,
Hausdorff measures and packing measures of limit sets of CIFSs of generalized complex continued fractions,
Journal of Difference Equations and Applications, 26 (2020), no. 1, pp. 104121.
pdf file.

J. Jaerisch and H. Sumi,
Spectral gap property for random dynamics on the real line and multifractal analysis of generalized Takagi functions,
30 pages, Comm. Math. Phys. 377, 136. (2020). pdf file.

J. Jaerisch and H. Sumi,
Multifractal formalism for generalised local dimension spectra of Gibbs measures on the real line,
J. Math.Anal.Appl.491(2020)124246.
pdf file.
 H. Sumi, Negativity of Lyapunov Exponents and Convergence of Generic Random Polynomial Dynamical Systems
and Random Relaxed Newton's Methods,
Comm. Math. Phys. 384, 15131583 (2021).
pdf file.

M. Comerford, K, Falk, R. Stankewitz, H. Sumi,
Uniformly perfect and hereditarily non uniformly perfect analytic
and conformal nonautonomous attractor sets,
Dyn. Syst. 36 (2021), no. 4, 631655.
pdf file.
 H. Sumi and T. Watanabe,
Noni.i.d. random holomorphic dynamical systems and the generic dichotomy,
Nonlinearity 35 (2022) 18571875.
pdf file.
Presentation files

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.
pdffile.
Curriculum Vitae

September 1970, Born in Otsu, Japan

1994 Bachelor degree in Faculty of Science, Kyoto University
(majoring mathematics)

1999 Ph. D. in Graduate School of Human and Environmental Studies,
Kyoto University.

19992005 Assistant Professor in
Department of Mathematics,
Tokyo Institute of Technology

20052017 Associate Professor in Department of Mathematics,
Graduate School of Science,
Osaka University

2017 Professor in Course of Mathematical Science,
Department of Human Coexistence, Graduate School of Human and Environmental Studies,
Kyoto University
Prize

2000 The MSJ Takebe Katahiro Prize for Encouragement of Young Researchers
(from The Mathematical Society of Japan)
[home page of Takebe Prize]

2012 Osaka University President Award for Encourgement (for research)

The 2019 MSJ Analysis Prize (from the Mathematical Society of Japan)
[The 2019 MSJ Analysis Prize]
[
2019 MSJ Analysis Prize Commemorative Talk, September 22, 2020, MSJ meeting, in Japanese]
Links

[
Conference ``Research on the Theory of Random Dynamical Systems and Fractal Geometry''
(August 29September 2, 2019) held at Kyoto University ]

[
Conference ``The Theory of Random Dynamical Systems and its Applications'' (February 19February 21, 2014)
held at Research Institute for Mathematical Sciences, Kyoto University ]

[
Complex Dynamics Conference of Academic Year 20112012 (January 23January 27, 2012)]

[
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]

[
2009 Complex dynamics conference ``Integrated Research of Complex Dynamics and Related Fields''
(December 14, 2009  December 18, 2009) homepage]

[
Rich Stankewitz home page]

[
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]

[
Dr. Johannes Jaerisch (Shimane Univ.) ]

[
Dr. Mao Shinoda (Kyoto Univ., JSPS Post Doc. Fellow) ]