**Teturo
KAMAE**

Nationality: Japanese

Date of Birth:

__Curriculum Vitae__** **

Graduated from Department of Chemistry: Tokyo University, March
1965

Master of Science in Mathematices: Tokyo University, March 1967

ph. D. in Mathematics: Osaka University, Sept. 1973

Research Officer: Institute of Statistical Mathematics, 1967--1968

Research Assistant: Department of Applied Mathematics, Osaka University,
1968--1972

Lecturer: Department of Mathematics, Osaka City University, 1972--1974

Associate Professor: Department of Mathematics, Osaka City University,
1974--1985

Professor: Department of Mathematics, Osaka City University, 1985--2005

Professor: Faculty of Economics,

Researcher: Osaka City University Advanced
Mathematical Institute, 2012-- (present position)

__List of Papers__** **

[1] Triangular
inequalities about Kolmogorov's complexity, Sugaku 21-3 (1969) pp.211-212 (in
Japanese)

[2] Spectrum of a
substitution minimal sets, J. Math. Soc.

[3] A topological
invariant of substitution minimal sets, J. Math. Soc.

[4] On unrecognizable
sets of numbers by finite automata, Sugaku 25-4 (1973) pp.365-367 (in Japanese)

[5] On Kolmogorov's
complexity and information, Osaka J. Math. 10-2 (1973) pp.305-307

[6] Subsequences of
normal sequences, Israel J. Math. 16-2 (1973) pp.121-149

[7] (with B. Weiss)

[8] Normal numbers and
ergodic theory, Proceedings of 3rd Japan-USSR Symposium on Probability Theory,
Lecture Notes in Mathematics 550, Springer-Verlag (1976) pp.253-269

[9] (with U. Krengel and
G. L. O'Brien) Stochasticinequalities on partially ordered spaces, Ann. Probability5-6 (1977) pp.899-912

[10]
(with J. Coquet and M. Mend\`es France) La mesure spectrale de certaines suites
arithm\'etiques, Bull. Soc. Math.

[11] Spectral properties
of arithmetic functions, S\'eminaire Delange-Pisot-Poitou 12 (1977)

[12] Mutual singularity
of spectra of dynamical systems given by "sum of digits" to different
bases, Soc. Math.France Ast\'erisque
49 (1977) pp.109-114

[13]
Infinite interval exchange transformation with positive entropy, S\'eminaire de
Probabilites II, Universit\'e de Rennes (1977)

[14] (with U. Krengel)
Stochastic partial ordering,Ann. Probability 6-6 (1978) pp.1044-1049

[15] Sum of digits to
different bases and mutual singularity of their spectral measures, Osaka J.
Math. 15 (1978) pp.569-574

[16] (with M. Mend\`es

[17] (with C. Christol,
M. Mend\`es-France and G. Rauzy) Suites alg\'ebriques, automatiques et
substitutions, Bull. Soc. Math.

[18] A simple proof of
the ergodic theorem using nonstandard analysis, Israel J. Math. 42-4 (1982)
pp.284-290

[19] Information of
relative pairwise comparisons, J. Math. Analysis \& Applications 97-2
(1983) pp.355-373

[20] A characterization
of weakly wondering sequences for nonsingular transformations, Commentarii
Math. Sancti Pauli 32-1 (1983) pp.55-59

[21] (with M. Fukui)
Information polynomials of graphs, Number Theory and Combinatorics, World
Scientific Publishing Co. (1985) pp.97-104

[22] (with Y. Ito and I.
Shiokawa) Point spectrum and Hausdorff dimension, Number Theory and
Combinatorics, World Scientific Publishing Co.(1985) pp.209-227

[23] (with Y. Dupain and
M. Mend\`es

[24] A characterization
of self-affine functions, Japan J. Applied Math. 3-2 (1986) pp.271-280

[25] Cyclic extensions of
odometer transformations and spectral disjointness, Israel J. Math. 59-1 (1987)
pp.41-63

[26] (with M. Keane) A
class of deterministic self-affine processes, Japan J. Applied Math. 7-2 (1990)
pp.183-195

[27] Number theoretic
problems involving two independent bases, Number Theory and Criptography (ed.
J. H. Loxton),¡¡London Math. Soc. Lecture
Note Series 154, Cambridge Univ. Press, 1990, pp.196-203

[28] (with T. Bedford)
Stieltjes integration and stochastic calculus with respect to self-affine
functions, Japan J.Industrial \& Applied Math. 8-3 (1991) pp.445-459

[29] (with J-M.

[30] (with M. Mend\`es

[31] Multiple search
games with nonmovable hyder, Nova J. Mathematics, Game Theory and Algebra 6-1
(1996) pp.45-54

[32] (with M. Keane) A
simple proof of the ratio ergodic theorem, Osaka J. Math. 34 (1997) pp.653-657

[33] Linear expansions, strictly
ergodic homogeneous cocycles and fractals, Israel J. Math. 106 (1998)
pp.313-337

[34] (with M. Dateyama)
On direct sum decomposition of integers and Y. Ito's conjecture, Tokyo J. Math.
21-2 (1998),¡¡pp.433-440

[35] (with Jun-ichi
Tamura \& Zhi-Ying Wen) Hankel
determinants for the Fibonacci word and Pad\'e approximation, Acta Arith.
LXXXIX.2 (1999), pp.123-161

[36] (with Nertila Gjini)
Coboundary on colored tiling space as Rauzy fractal, Indagationes Mathematicae
10-3 (1999), pp.407-421

[37] Stochastic analysis based on deterministic
Brownian motion, Israel J. Math. 125
(2001), pp.317-346

[38] (with J-P. Allouche,
J-M. Deshouillers and T. Koyanagi) Automata, algebraicity and distribution of sequences of powers, Ann. Inst. Fourier 51-3 (2001), pp.687-705

[39] (with Luca Zamboni) Sequence entropy and the
maximal pattern complexity of infinite words, Ergodic Theory and¡¡Dynamical Systems 22-4 (2002), pp.1191-1199

[40] (with Luca Zamboni) Maximal pattern complexity
for discrete systems, Ergodic Theory and Dynamical Systems 22-4 (2002),
pp.1201-1214

[41] (with Xue Yu-Mei) Two dimensional word with 2k
maximal pattern complexity, Osaka J. Math. 41 (2004), pp.257-265

[42] Numeration systems,
fractals and stochastic processes, Israel J. Math. 149 (2005), pp.87-135 (all
the results are included in [50])

[43] (with Rao Hui) Maximal pattern
complexity over $\ell$ letters¡¤European
J. Combinatorics 27 (2006), pp.125-137

[44] (with Hayato
Takahashi) Statistical
problems related to irrational rotations, Annals of the

[45] (with Rao Hui and
Xue Yu-Mei) Maximal pattern
complexity of 2-dimensional words, Theoretical Computer Science 359 (2006),
pp.15-27

[46] Maximal pattern complexity
as topological invariants
(preprint)

[47] (with Nertila Gjini,
Tan Bo and Xue Yu-Mei) Maximal
pattern complexity for Toeplitz words, Ergodic Theory and Dynamical Systems
26 (2006), pp. 1-14

[48] (with Hui RAO, Bo
TAN and Yu-Mei XUE) Language
Structure of Pattern Sturmian Words, Discrete Mathematics 306 (2006), pp.
1651-1668

[49] Numeration systems
as dynamical systems – Introduction, in Dynamics
& Stochastics, Institute of Mathematical Statistics Lecture Notes – Monograph Series vol. 48,

[50] Numeration systems as
dynamical systems (new version of numeration systems) (preprint)

[51] Uniform Sets and Complexity
(Error Corrected), Discrete Mathematics 309 (2009), pp.3738-3747¡¡(doi:10.1016/j.disc.2008.10.001)

[52] (with Hui RAO, Bo
TAN and Yu-Mei XUE) Super-stationary
set, Subword problem and the Complexity (Error Corrected), Discrete
Mathematics 309 (2009), pp.4417-4427 (doi:10.1016/j.disc.2009.02.001)

[53] Mixing properties of the
numeration systems coming from weighted substitutions, Ergodic Theory and
Dynamical Systems 30 (2009). pp.1111-1118 (doi:10.1017/S0143385709000510)

[54] (with Yu-Mei XUE) Partitions by congruent
sets and optimal positions, Ergodic Theory and Dynamical Systems 31 (2011),
pp.613-629 (doi:10.1017/S0143385709001175)

[55] Uniform sets and
super-stationary sets over general alphabets, Ergodic Theory and Dynamical
Systems 31 (2011), pp.1445-1461 (doi:10.1017/S014338571000074X¡Ë

[56] (with Pavel V.
Salimov) On maximal
pattern complexity of some automatic words, Ergodic Theory and Dynamical
Systems 31 (2011), pp.1463-1470 (doi:10.1017/S0143385710000453)

[57] (with S. V.
Avgustinovich, A. E. Frid and P. V. Salimov) Infinite permutations of
lowest maximal pattern complexity, Theoretical Computer Science 412 (2011),
pp.2911-2921 (doi:10.1016/j.tcs.2010.12.062)

[58] Behavior of various
complexity functions, Theoretical Computer Science 420 (2012), pp.36-47
(doi:10.1016 /j.tcs.2011.11.1012)

[59] (with Yu-Mei XUE) Maximal pattern
complexity, dual system and pattern recognition, Theoretical Computer
Science 457 (2012), pp.166-173 (doi:10.1016/j.tcs.2012.06.033)

[60] Infinitesimal geometry
and superstationary factors of dynamical systems, Topology and its
Applications 160 (2013), pp.844-861
(doi:10.1016/j.topol.2013.02.010)

[61]
(with Yu-Mei XUE) Multifractal
analysis for a class of homogeneous Moran constructions, Chaos, Solitons
and Fractals 53 (2013), pp.52-59 (doi:10.1016/j.chaos.2013.05.006)

[62] (with STEVEN
WIDMER and LUCA Q. ZAMBONI) Abelian maximal pattern
complexity of words, Ergodic Theory and Dynamical Systems 35
(2015), pp.142-151 (doi:10.1017/etds.2013.51)

[63]
(with Yu-Mei XUE) An easy criterion
for randomness, Sankhya A 77-1 (2015), pp.126-152 (doi:10.1007/s13171-014-0054-3)

[64]
(with Yu-Mei XUE) Local time of self-affine
sets of Brownian motion type and the jigsaw puzzle problem, Journal of Mathematical
Analysis and Applications 419 (2014), pp.79–93 (doi:10.1016/j.jmaa.2014.04.018)

[65] (with Dong Han Kim) A characterization of eventually periodicity, Theoretical Computer Science 581 (2015), pp.1-8 (doi:10.1016/j.tcs.2015.02.039)

[66] (with Emilie Charlier, Svetlana Puzynina and Luca Q. Zamboni) Infinite Self-Shuffling Words, Journal of Combinatorial Theory (Series A) 128 (2014) pp.1-40 (doi:10.1016/j.jcta.2014.07.008)

[67]
(with Li PENG) Spectral measure of the
Thue-Morse sequence and the dynamical system and random walk related to it,
Ergodic Theory and Dynamical Systems 36 (2016), pp.1247-1259 (doi:10.1017/etds.2014.121)

[68]
(with Li PENG) Hausdorff dimension of the
level sets of self-affine functions, Journal of Mathematical Analysis and Applications¡¡423
(2015), pp.1400–1409¡¡(doi:10.1016/j.jmaa.2014.10.058)

[69] (with Jun
Luo and Bo TAN) A Glueing Lemma for
Iterated Function Systems, FRACTALS 23-2 (to appear), (doi:10.1142/S0218348X1550019X)

[70] Entropy estimate by a
randomness criterion, Ergodic Theory and Dynamical Systems 37-3 (2017), 802-823 (doi:10.1017/etds.2015.79)

[71] (with Yu-Mei XUE) Local time of
self-affine sets of Brownian motion type –
revisited, Journal of Mathematical Analysis and Applications
437-1 (2016), 638-644

[72] (with Yu-Mei XUE) H\"older
equivalence of homogeneous Moran sets, Publicationes Mathematicae Debrecen 89/1-2 (2016), pp.233-242¡¡(doi:
10.5486/PMD.2016.7538)

[73] (with Dong Han Kim and Yu-Mei Xue) Randomness criterion
\Sigma and its applications, Sankhya A (to appear)