# LIST of ARTICLES

1. The proof of weak Bernoulli property of linear mod.1 transformation in statistical mechanical method, master thesis University of Tokyo (1973).
2. Isomorphism of a piecewise linear transformation to a Markov automorphism, Publ. Res. Inst. Math. Sci., Kyoto University, vol. 13, 1-16 (1977). With Sh.Ito.
3. The construction of a dynamical system of a model in 1-dimensional statistical mechanics, Sci. Rep. Tokyo Kyoiku Daigaku Sec. A, vol. 13, 257-268 (1977).

### 1980-1989

1973-1979
1980-1989-
1990-1999
2000-2009
2010-2014
2015-
4. Dynamical system with continuous states and relative free energy, Tokyo J. Math., vol. 4, 177-191 (1981). With M.Kowada.
5. Relative free energy and its application to speed change model, Tsukuba J. Math., vol. 5, 1-14 (1981). With M.Kowada.
6. The extension of Sarkovskii's results and the topological entropy in unimodal transformations, Tokyo J. Math., vol. 4, 133-152 (1981).
7. On the decay of correlation for piecewise monotonic mappings I, Tokyo J. Math., vol. 8, 389-414 (1985).
8. Spectra of correlation for piecewise linear transformations, Mem. Natl. Def. Acad. Jpn., vol. 25, 99-108 (1985).
9. On the critical phenomena for piecewise linear transformations, Dynamical systems and nonlinear oscillations (Advance Series in Dynamical Systems, World Scientific), vol. 1, 179-193 (1985).
10. On the decay of correlation for piecewise monotonic mappings II, Tokyo J. Math., vol. 9,135-161 (1986).
11. On the decay rate of correlation for piecewise linear transformations Lecture Note in Mathematics 1299, 332-338, Springer Verlag (1986).
12. On the Fredholm determinant of a piecewise linear transformation, Dynamical systems and nonlinear oscilations (Advance Series in Dynamical Systems, World Scientific), vol. 5, 117-121 (1987).
13. On the Fredholm determinant of a piecewise linear transformation, Theor. Computor Sci., vol. 65, 243-248 (1989).

### 1990-1999

1973-1979
1980-1989
1980-1999
2000-2009
2010-2014
2015-
14. Fredholm determinant for piecewise linear transformations, Osaka J. Math., vol. 27, 81-116 (1990).
15. Fredholm matrices and zeta function for piecewise monotonic transformations, Dynamical systems and related topics(Advance Series in Dynamical Systems, World Scientific), vol. 9, 388-400 (1990).
16. Fredholm determinant for piecewise monotonic transformations, Osaka J. Math., vol. 29, 497-529 (1992)(Doctor Thesis).
17. On the intermittency of a piecewise linear map(Takahashi model), Tokyo J. Math., vol. 16, no.2, 411-428 (1993).
18. On the convergence of the spectrum of Perron-Frobenius operator, Tokyo J. Math., vol. 17, no.2., 1-19(1994).
19. Perron-Frobenius operator for higher dimensional piecewise linear transformations, Proceeding of the international Conference on Dynamical Systems and Chaos, vol. 1, World Scientific, 178-181(1995).
20. Fredholm Matrix and Zeta Functions for 1-dimensional Mappings, Algorithms, Fractals, and Dynamics(1995), Proceedings of Algorithms, Fractals and Dynamics in Kyoto, 161-168(1995)
21. Fredholm determinant for piecewise linear transformations on a plane, Tokyo J. Math. 21 No.2, 477-510, 1998
22. Zeta function and Perron-Frobenius operator of piecewise linear transformations on Rk, Tokyo Journal of Math. vol.18, 401-416(1995).
23. Dynamical system on Cantor set, Tokyo J. Math. vol.21, 217-232(1998)
24. One-dimensional dynamical system and Fractals, TECHNICAL REPORT OF IEICE, vol. NLP97 No.591, 81-87 (1998)
25. Fredholm determinant for higher dimensional piecewise linear transformations, Japanese Journal of Mathematics, Vol. 25 No.2, 317-342(1999)
26. Low discrepancy sequences generated by piecewise linear Maps, Monte Carlo methods and Applications, vol. 4 No.2, 141-162(1998).
27. Discrepancy of sequences generated by piecewise monotone Maps, Monte Carlo Methods and Appl., vol. 5 No.1, 55-68(1999)

### 2000-2009

28. 1次元写像の多重混合性について，京都大学数理解析研究所講究録1127,60-67
29. Cantor sets generated by Piecewise linear map, The Inst. of Natural Sciences Nihon Univ., vol.35, 1-27(2000)
30. Higher order mixing property of piecewise linear transformations, Discrete and Continuous Dynamical systems, vol. 6, 915--934(2000)
31. Pseudo random sequences generated by piecewise linear maps from the view point of dynamical system, Mathematics and Computers in Simulation, vol. 55, 177-189(2001)
32. Brownian motion generated by one--dimensional dynamical systems. The Inst. of Natural Sciences Nihon Univ.
33. Dynamical Systems on fractals in a plane, Osaka J. Math., vol. 38, 1-28 (2001)
34. 高次元の low discrepancy sequence の構成, 数理研究所講究録1240, 125-133
35. Construction of two dimensional low discrepancy sequences, Monte Carlo methods and Applications vol. 8 No.2, 159-170(2002)
36. 重症頭部外傷の治療の現状:手術群・非手術群比較の観点から，山木垂水(京都九条病院)，藤本正人(済生会滋賀県病院)，森 真，神経外傷25 No.3，172-181(2002)
37. Fractal と Perron-Frobenius 作用素，数理研究所講究録1333, 57-65
38. Hausdorff Dimension of a Cantor set on R1, with Yuko Ichikawa, Mariko Ohno, Tokyo J. Math. vol.26, No.2, 371-390(2003)
39. 大学教育におけるTA制度の実態に関する総合研究，北野秋男，関口なほ子，中里勝芳， 大学教育学会誌25巻第2号(2003年11月)
40. 山木垂水，藤本正人，森　真，重症頭部外傷の治療成績ー頭部外傷データバンク検討委員会報告書を基にー，脳神経外科ジャーナル　 vol. 13, No.2(2004)
41. Hausdorff Dimension as Thermodynamical Formlism, Proceedings of the Institute of Natural sciences, Nihon University, vol. 39,303-316(2004)
42. Low discrepancy sequences generated by dynamical system, 数理研究所講究録1404, 64-67
43. Discrepancy of van der Corput sequences generated by piecewise linear transformations, Yuko Ichikawa and Makoto Mori, Monte Carlo Methods and Applications, vol.10(2004), N2, 107-116.
44. Discrepancy of sequences generated by dynamical system, Monte Carlo Methods and Applications, Vol. 10 No.3-4, 455-459(2004)
45. Hausdorff dimension of trees generated by piecewise linear transformations. Tokyo J. Math. vol. 28, no.1, 249-258(2005)
46. Construction of 3 dimensional low discrepancy sequences, Monte Carlo Methods and Applications, vol.11 No.2, 163-174(2005)
47. Mixing properties and pseudo random sequences, Dynamic and Stochastics, Lecture Notes--Monograph series 48, 189--197(2006)
48. On Rotation Number of Dynamical Systems, Proceedings of The Institute of Natural Sciences, Nihon University, No.42, 183-195(2007)
49. Representations of Cuntz algebras on fractal sets, with Osamu Suzuki and Yasuo Watatani, Kyushu Journal of Math. 61, 443-456 (2007)
50. Low discrepancy sequences generated by dynamical systems, Advanced Studies in Pure Mathematics, 49, 245--262(2007)
51. Spectra of Perron-Frobenius operator and new construction of two dimensional low discrepancy sequences, Monte Carlo Methods and Applications, col. 14, 53-74(2008)
52. Low discrepancy sequences, 数理解析研究所講究録1620, 204-210(2009)
1973-1979
1980-1989
1990-1999
2000-2009
2010-2014
2015-

### 2010-

53. New Construction of Two Dimensional Low Discrepancy Sequences (with Masaki Mori), Proceedings of the Institute of Natural Sciences, Nihon University 47,449--462, 2012
54. Dynamical system generated by algebraic method and low discrepancy sequences, Monte Carlo Methods and Applications, vol.18 no4, 327-351,2012 Dec.
55. 力学系のエルゴード性と疑似乱数, 数理研究所講究録1852, 225--234(2013)
1973-1979
1980-1989
1990-1999
2000-2009
2010-2014
2015-

### 2015-

56. Spectra of Perron-Frobenius Operator for $\beta$-Transformations on Piecewise Continuous Functions， Proceedings of the Institute of Natural Sciences, Nihon University, 50 255-274 (2015)
57. Kazuhiro Ichihara, Makoto Mori, Ken-ichi Yosshida, On partitions of components for closed random braids, RIMS研究集会報告集 ,2015年5月,1-17
58. Spectra of Perron-Frobenius operator on piecewise continuous functions, Proceedings of the Institute of Natural Sciences, Nihon University, 51, 299-315 (2016)

Last revised on April. 16,
Copyright Makoto Mori 2012 all right reserved