List of Papers
Teturo Kamae[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. Japan 22-4
(1970) pp.567-578[3] A topological invariant of substitution minimal sets, J. Math. Soc.
Japan 24-2 (1972) pp.285-306[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.121149[7] (with B. Weiss) Normal numbers and selection rules, Israel J.Math.
21-2-3 (1975) pp.101-110[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. Mendès France) La mesure spectrale decertaines suites arithmétiques, Bull. Soc. Math. France 105 (1977)
pp.369-387[11] Spectral properties of arithmetic functions, Séminaire Delange-PisotPoitou 12 (1977)[12] Mutual singularity of spectra of dynamical systems given by ”sumof digits” to diﬀerent bases, Soc. Math.France Astérisque 49 (1977)
pp.109-114[13] Infinite interval exchange transformation with positive entropy, Séminairede Probabilites II, Université de Rennes (1977)[14] (with U. Krengel) Stochastic partial ordering,Ann. Probability 6-6(1978) pp.1044-10491

[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. Mendès France) Van der Corput’s diﬀerence theorem, Israel J. Math. 31-3-4 (1978) pp.335-342[17] (with C. Christol, M. Mendès-France and G. Rauzy) Suites algébriques,automatiques et substitutions, Bull. Soc. Math. France 108 (1980)
pp.401-419[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 nonsingulartransformations, Commentarii Math. Sancti Pauli 32-1 (1983) pp.55-59[21] (with M. Fukui) Information polynomials of graphs, Number Theoryand 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 PublishingCo.(1985) pp.209-227[23] (with Y. Dupain and M. Mendès France) Can one measure the temperature of a curve?, Archive for Rational Mechanics and Analysis 94-2(1986) pp.155-163[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, JapanJ. 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 withrespect to self-aﬃne functions, Japan J.Industrial & Applied Math. 8-3(1991) pp.445-459[29] (with J-M. Dumont and S. Takahashi) Minimal cocycleswith scaling
property and substitutions, Israel J. Math. 95 (1996) pp.393-410[30] (with M. Mendès France) A continuous family of automata: theIsing automata, Annales Institut Henri Poincaré 64-3(1996) pp.349-372[31] Multiple search games with nonmovable hyder, Nova J. Mathemat-2

ics, Game Theory and Algebra 6-1 (1996) pp.45-54[32] (with M. Keane) A simple proof of the ratio ergodic theorem, OsakaJ. 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 andY. 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 Padé 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 patterncomplexity 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 patterncomplexity, Osaka J. Math. 41 (2004), pp.257-265[42] Numeration systems, fractals and stochastic processes, Israel J.
Math. 149 (2005), pp.87-135[43] (with Rao Hui) Maximal pattern complexity over ℓ letters，European J. Combinatorics 27 (2006), pp.125-137[44] (with Hayato Takahashi) Statistical problems related to irrationalrotations, Annals of the Institute of Statistical Mathematics vol. 58(2006) pp.573-593[45] (with Rao Hui and Xue Yu-Mei) Maximal pattern complexity of 2dimensional 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 Structure3

of Pattern Sturmian Words, Discrete Mathematics 306 (2006), pp.16511668[49] Numeration systems as dynamical systems -Introduction, in Dynamics & Stochastics, Institute of Mathematical Statistics Lecture NotesMonograph Series vol. 48, Beechwood, Ohio, USA, 2006[50] Numeration systems as dynamical systems (new version of numeration systems) (preprint)[51] Analysis of opposition and cooperation in game theory, Sugaku
Tusin 11-4 (2007)，pp.6-20 (in Japanese)[52] Uniform Sets and Complexity, Discrete Mathematics 309 (2009),
pp.3738-3747[53] (with Hui RAO, Bo TAN and Yu-Mei XUE) Super-stationary set,
Subword problem and the Complexity, Discrete Mathematics 309 (2009),
pp.4417-4427[54] Mixing properties of the numeration systems coming from weighted
substitutions, Ergodic Theory and Dynamical Systems 30 (2009). pp.11111118[55] (with Yu-Mei XUE) Partitions by congruent sets and optimal positions, Ergodic Theory and Dynamical Systems 31 (2011), pp.613-629[56] Uniform sets and super-stationary sets over general alphabets, Ergodic Theory and Dynamical Systems 31 (2011), pp.1445-1461[57] (with Pavel V. Salimov) On maximal pattern complexity of some
automatic words, Ergodic Theory and Dynamical Systems 31 (2011),
pp.1463-1470[58] (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[59] Behavior of various complexity functions, Theoretical Computer Science 420 (2012), pp.36-47[60] (with Yu-Mei XUE) Maximal pattern complexity, dual system andpattern recognition, Theoretical Computer Science 457 (2012), pp.166173[61] Infinitesimal geometry and super-stationary factors of dynamicalsystems, Topology and its Applications 160 (2013), pp.844-861[62] (with Yu-Mei XUE) Multifractal analysis for a class of homogeneous
Moran constructions, Chaos, Solitons and Fractals 53 (2013), pp.52-59[63] (with Steven WIDMER and Luca Q. ZAMBONI) Abelian maximal
pattern complexity of words, Ergodic Theory and Dynamical Systems354

(2015), pp.142-151 (doi:10.1017/etds.2013.51)[64] (with Yu-Mei XUE) An easy criterion for randomness, Sankhya A
77-1 (2015), pp.126-152 (doi:10.1007/s13171-014-0054-3)[65] (with Yu-Mei XUE) Local time of self-aﬃne sets of Brownian motion
type and the jigsaw puzzle problem, Journal of Mathematical Analysisand Applications 419 (2014), pp.79-93[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 andthe dynamical system and random walk related to it, Ergodic Theory andDynamical Systems 36 (2016), pp.1247-1259 (doi:10.1017/etds.2014.121)[68] (with Li PENG) Hausdorﬀ dimension of the level sets of self-aﬃnefunctions, Journal of Mathematical Analysis and Applications 423 (2015),
pp.1400-1409[69] (with Jun Luo and Bo TAN) A Glueing Lemma for Iterated Function
Systems, Fractals 23-2 (to appear), (doi:10.1142/S0218348X1550019X)[70] (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)[71] Entropy estimate by a randomness criterion, Ergodic Theory andDynamical Systems 37-3 (2017), 802-823 (doi:10.1017/etds.2015.79)[72] (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[73] (with Yu-Mei XUE) Hölder equivalence of homogeneous Moran sets,Publicationes Mathematicae Debrecen 89/1-2 (2016), pp.233-242 (doi:10.5486/PMD.2016.7538)[74] (with Dong Han Kim and Yu-Mei Xue) Randomness criterion Σ andits applications, Sankhya 80-A, Part 2 (2018), 356-384[75] (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[76] (with Xiaowen Wang) Selection rules preserving normality, Israel J.
Math. 232 (2019) pp.427442[77] (with Yu Zheng and Li Peng) Spectral properties of pattern sequences of general degrees, Nonlinearity 34 (2021) pp.34113428

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