**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 Metropolitan University (changed the name from
Osaka City University in 2023)

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) Stochastic
Inequalities 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 France) Van der Corput's
difference theorem, Israel J. Math.

[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 $\ell$ lettersCEuropean
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/S014338571000074Xj

[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 (2015),
(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 80-2 (2018), pp.356-384

[74] (with Yu Zheng and
Li Peng) Characterization of
noncorrelated pattern sequences and correlation dimensions, Discrete and
Continuous Dynamical Systems 38-10 (2018) pp.5085-5103 (doi:10.3934/dcds.2018223)

[75] (with Xiaowen Wang) Selection rules preserving
normality, Israel J. Math. 232 (2019) pp.427–442

[76] (with Yu Zheng and Li Peng) Spectral properties
of pattern sequences of general degrees, Nonlinearity **34 **(2021) pp.3411–3428

[77] (with S. Akiyama) Width deviation of convex polygons, Discrete & Computational Geometry (to appear)

[78] Dynamical
system at infinity, super-stationarity, uniform complexity and pattern
recognition (survey of the talk at RIMS (Kyoto University), Oct.,2023)