Dynamical systems and number theoretical problems coming from compactifications of digital representations of the real numbers

2008 Fiscal Year Final Research Report

• Project/Area Number: 18540151
• 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: Matsuyama University
• Principal Investigator: KAMAE Teruro Matsuyama University, 経済学部, 教授 (80047258)
• Project Period (FY): 2006 – 2007
• Keywords: numeration system / colored tiling / homogeneous cocycle / 一様集合 / 最適位置

Research Abstract

本研究の目的は,実数のデジタル表示にともなうコンパクト化の考察であった。とくに,連続なスケーリングを許すような数体系と,この上の同次コサイクルを考察し,興味あるフラクタル関数や自己相似確率過程を導いた。また,派生した問題である一様集合の解析で顕著な結果が得られた

Research Products

• [Journal Article] Maximal pattern complexity over l letters (2006)
  • Author(s): T.Kamae, Rao Hui
  • Journal Title: European J. Combinatorics 27 Pages: 125-137
• [Journal Article] Statistical problems related to irrational rotations (2006)
  • Author(s): T.Kamae, Hayato Takahashi
  • Journal Title: Annals of the Institute of StatisticalMathematics vol. 58 Pages: 573-593
• [Journal Article] Maximal pattern complexity for 2-dimensional words (2006)
  • Author(s): T.Kamae, Rao Hui, Xue Yu-Mei
  • Journal Title: Theoretical Computer Science 359 Pages: 15-27
• [Journal Article] Maximal pattern complexity for Toeplitz words (2006)
  • Author(s): T.Kamae, Nertila Gjini, Tan Bo, Xue Yu-Mei
  • Journal Title: Ergodic Theory and Dynamical Systems 26 Pages: 1-14
• [Journal Article] Language Structure of Pattern Sturmian Word (2006)
  • Author(s): T.Kamae, Hui RAO, Bo TAN, Yu-Mei XUE
  • Journal Title: Discrete Mathematics 306 Pages: 1651-1668
• [Journal Article] Uniform Sets and Complexity
  • Author(s): T.Kamae
  • Journal Title: Discrete Mathematics DOI 10.1016/j.disc.2008.10.001
• [Journal Article] Super-stationary set, Subword problem and the Complexity
  • Author(s): T.Kamae, Hui RAO, Bo TAN, Yu-Mei XUE
  • Journal Title: Discrete Mathematics DOI 10.1016/j.disc.2009.02.001
• [Journal Article] Mixing properties of the numeration systems coming from weighted substitutions
  • Author(s): T.Kamae
  • Journal Title: Ergodic Theory and Dynamical Systems to appear
• [Presentation] Uniform sets and complexity (2009)
  • Author(s): T.Kamae
  • Organizer: The 6 <th> International conference on Nonlinear Analysis and Convex Analysis
  • Place of Presentation: 東京工業大学
  • Year and Date: 20090300
• [Presentation] Uniform complexity functions (2008)
  • Author(s): T.Kamae
  • Organizer: First joint meeting of Chinese Mathematical Society and American Mathematical Society
  • Place of Presentation: 復旦大学(上海)
  • Year and Date: 20081200
• [Book] Institute of Mathematical Statistics Lecture Notes - Monograph Series vol. 48, Beechwood, Ohio, USA (2006)
  • Author(s): T.Kamae
  • Publisher: Numeration systems as dynamical systems - Introduction, in Dynamics & Stochastics