Characterization related to Rauzy fractals of substitutions

• Project/Area Number: 19740056
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Chuo University
• Principal Investigator: EI Hiromi Chuo University, 理工学部, 助教 (60333051)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥1,020,000 (Direct Cost: ¥900,000、Indirect Cost: ¥120,000); Fiscal Year 2008: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000); Fiscal Year 2007: ¥500,000 (Direct Cost: ¥500,000)
• Keywords: サブスティテューション / 記号力学系 / フラクタル / タイリング / 自由群 / エルゴード理論

Research Abstract

ランク3以上のサブスティテューションに対し,その可逆性とサブスティテューションに対して決まる指標との関係を与えた.また,可逆性と連結性について,ランク2の結果の反例となる,非可逆(可逆)であるがR-フラクタルが連結(非連結)となる例を発見した.自由群上の同型写像については,サブスティテューションの場合と同様に扱うことのできるクラスを設定し,R-フラクタル,タイリングの生成方法を与えた.

Research Products

• [Journal Article] Tilings of a Riemann surface and cubic Pisot numbers (2007)
  • Author(s): 榎本文彦, 江居宏美, 古門麻貴, 伊藤俊次
  • Journal Title: Hiroshima Math. J., vol. 37, no. 2 Pages: 181-210
  • NAID: 110006311484
  • Peer Reviewed
• [Journal Article] On サブスティテューション invariant sturmian words : an application of Rauzy fractals (2007)
  • Author(s): Valerie BERTHE, 江居宏美, 伊藤俊次, Hui RAO
  • Journal Title: Theoret. Informatics Appl. vol. 41, no. 3 Pages: 329-349
  • Peer Reviewed
• [Presentation] Atomic surfaces generated by automorphisms of rank 2 in some class (2008)
  • Author(s): 江居宏美
  • Organizer: International Workshop on Fractal Geometry and Ergodic Theory
  • Place of Presentation: Beijing Technology University and Tsinghua Uiversity (China)
  • Year and Date: 2008-11-02
• [Presentation] Connectedness of atomic surfaces generated by invertible substitutions (2008)
  • Author(s): 江居宏美
  • Organizer: Combinatorial and Computational aspects of Tilings
  • Place of Presentation: Imperial College London (England)
  • Year and Date: 2008-07-30
• [Presentation] Connectedness of atomic surfaces generated by invertible substitutions (2008)
  • Author(s): 江居宏美
  • Organizer: Combinatorial and Computational aspects of Tilings
  • Place of Presentation: Imperial College London
  • Year and Date: 2008-07-30
• [Presentation] Stepped surfaces generated by automorphisms of the free group (2007)
  • Author(s): 江居宏美
  • Organizer: Journees de Numeration
  • Place of Presentation: Graz University of Technology (Austria)
  • Year and Date: 2007-04-16
• [Presentation] Stepped surfaces generated by automorphisms of the free group (2007)
  • Author(s): 江居 宏美
  • Organizer: Journees de Numeration
  • Place of Presentation: Austria, Graz
  • Year and Date: 2007-04-16