Teturo KAMAE

Nationality: Japanese
Date of Birth: 25 October, 1941

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, Matsuyama University, 2005--2010

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. 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.121-149

[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) 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. France 105 (1977) pp.369-387

[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. 31-3-4 (1978) pp.335-342

[17] (with C. Christol, M. Mend\`es-France and G. Rauzy) Suites alg\'ebriques, 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 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 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, 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. Dumont and S. Takahashi) Minimal cocycles with scaling property and substitutions, Israel J. Math. 95 (1996) pp.393-410

[30] (with M. Mend\`es France) A continuous family of automata: the Ising automata, Annales Institut Henri Poincar\'e 64-3(1996) pp.349-372

[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CEuropean J. Combinatorics 27 (2006), pp.125-137

[44] (with Hayato Takahashi) Statistical problems related to irrational rotations, 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 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, Beechwood, Ohio, USA, 2006 (all the results are included in [50])

[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j

[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.7993 (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.14001409@(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.427442

[76] (with Yu Zheng and Li Peng) Spectral properties of pattern sequences of general degrees, Nonlinearity 34 (2021) pp.34113428

[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)