On the Perron-Frobenius operator associated with dynamical systems in higher dimensional space and pseudo-random sequences

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20540139
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Nihon University
• Principal Investigator: MORI Makoto Nihon University, 文理学部, 教授 (60092532)
• Project Period (FY): 2008 – 2012
• Keywords: 疑似乱数 / ペロンフロベニウス作用素

Research Abstract

高次元の力学系に対応するペロンフロベニウス作用素のスペクトルの研究とそれを用いた疑似乱数の構成を行い,疑似乱数のdiscrepancyをペロンフロベニウス作用素のスペクトルにより評価する.

Research Products

• [Journal Article] Low discrepancy sequences (2009)
  • Author(s): Makoto Mori
  • Journal Title: 数理解析研究所講究録 1620 Pages: 204-210
  • Peer Reviewed
• [Journal Article] Spectra of Perron-Frobenius operator and new construction of two dimensional low discrepancy sequences (2008)
  • Author(s): Makoto Mori
  • Journal Title: Monte Carlo Methods and Applications vol.14 Pages: 53-74
  • Peer Reviewed
• [Journal Article] New Constructiion of two dimensional Low Discrepancy Sequences}
  • Author(s): Makoto Mori, Masaki Mori
  • Journal Title: Proceeding of Lorentz Center, Leiden, Holland 投稿中
  • Peer Reviewed
• [Presentation] 有限体から作る力学系について (2011)
  • Author(s): 森真, 森真樹
  • Organizer: 日本数学会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2011-03-20
• [Presentation] 高次元の疑似乱数の新しい構成 (2011)
  • Author(s): 森真, 森真樹
  • Organizer: Dynamics of Complex Systems
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-03-07
• [Presentation] Dynamical systems generated by algebraic method and low discrepancy sequences (2010)
  • Author(s): 森真
  • Organizer: Information and Randomness 2010
  • Place of Presentation: Pucon, Chile
  • Year and Date: 2010-12-11
• [Presentation] Random numbers generated by Dynamical system (2010)
  • Author(s): 森真
  • Organizer: Colloquium in Rouen
  • Place of Presentation: Rouen University
  • Year and Date: 2010-01-28
• [Presentation] 力学系と疑似乱数 (2010)
  • Organizer: 計算による数理科学の展開2010
  • Place of Presentation: 神戸大学
  • Year and Date: 2010-01-08
• [Presentation] A strategy of constructing d-dimensional low discrepancy sequences (2009)
  • Author(s): Makoto Mori
  • Organizer: Measurable and Topological Dynamical Systems in Asia
  • Place of Presentation: Ajou University(韓国)
  • Year and Date: 2009-06-19
• [Presentation] Pseudo random sequences generated by dynamical systems (2009)
  • Author(s): 森真
  • Organizer: Numeration : Mathematics and Computer Science
  • Place of Presentation: CIRM,(France)
  • Year and Date: 2009-03-24
• [Presentation] Pseudo random numbers and ergodic theory (2008)
  • Author(s): Makoto Mori
  • Organizer: School of Information and Randomness 2008
  • Place of Presentation: チリ大学
  • Year and Date: 2008-12-16
• [Presentation] On random numbers generated by dynamical systems (2008)
  • Author(s): Makoto Mori
  • Organizer: Conference on Fractal Geometry and Ergodic Theory
  • Place of Presentation: 北京科学技術大学
  • Year and Date: 2008-11-02
• [Presentation] Spectra of Perron--Frobenius operator and discrepancy of random numbers generated by dynamical system (2008)
  • Author(s): 森真
  • Organizer: Dynamics of complex systems 2008
  • Place of Presentation: 北海道大学
  • Year and Date: 2008-09-03
• [Presentation] 確率数値解析に於ける諸問題の研究 (2008)
  • Author(s): 森真
  • Organizer: Low discrepancy sequences
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-07-08
• [Book] 入門力学系 (2009)
  • Author(s): 森真, 水谷正大共著
  • Total Pages: 304
  • Publisher: 東京図書