Study on boundaries of Coxeter groups anddynamical structure on the chain recurrent set

• Project/Area Number: 22540098
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Jikei University School of Medicine
• Principal Investigator: YOKOI Katsuya 東京慈恵会医科大学, 医学部, 教授 (90240184)
• Co-Investigator(Kenkyū-buntansha): HOSAKA Tetsuya 静岡大学, 理学部, 准教授 (50344908) ; YAMADA Takumi 島根大学, 総合理工学部, 准教授 (40403117)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 位相幾何学 / 位相的力学系 / 次元論 / 幾何学的群論 / 回帰性 / 極限集合 / 力学系 / コクセター群 / CAT(0)群 / CAT(0)空間 / ケーラー多様体 / 鎖回帰集合 / 漸近的トポロジー / 漸近的次元 / 距離空間

Research Abstract

We study recurrence properties for the non-autonomous discrete system given by a sequence of continuous self-maps on a compact metric space. In particular, our attention is paid to the case when the sequence of maps converges uniformly to a map. We investigate the structure and behavior of a limit set of the sequence by a dynamical property of the limit map. We also create a perturbation of the sequence whose non-wandering set has small measure.

Research Products

• [Journal Article] Recurrence properties of a class of nonautonomous discrete systems (2013)
  • Author(s): Katsuya Yokoi
  • Journal Title: Bulletin of the Belgian Mathematical Society Simon Stevin Volume: to appear
  • Peer Reviewed
• [Journal Article] Asymptotic dimension and boundary dimension of proper CAT(0) spaces (2013)
  • Author(s): Naotsugu Chinen and Tetsuya Hosaka
  • Journal Title: Tsukuba Journal of Mathematics Volume: to appear
  • NAID: 120006582859
  • Peer Reviewed
• [Journal Article] On a new class of rigid Coxeter group (2013)
  • Author(s): Tetsuya Hosaka
  • Journal Title: Hokkaido Mathematical Journal Volume: to appear
  • Peer Reviewed
• [Journal Article] Reconstructible graphs, simplicial flag complexes of homology manifolds and associated right-angled Coxeter groups (2013)
  • Author(s): Tetsuya Hosaka
  • Journal Title: Osaka Journal of Mathematics Volume: to appear
  • NAID: 120005830508
  • Peer Reviewed
• [Journal Article] Parabolic subgroups of Coxeter groups acting by reflections on CAT(0) spaces (2012)
  • Author(s): Tetsuya Hosaka
  • Journal Title: Rocky Mountain Journal of Mathematics Volume: 42 Pages: 1207-1214
  • Peer Reviewed
• [Journal Article] On splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature (2012)
  • Author(s): Tetsuya Hosaka
  • Journal Title: Mathematische Zeitschrift Volume: 272 Pages: 1037-1050
  • Peer Reviewed
• [Journal Article] Holomorphic vector fields of compact pseudo-Kahler manifolds (2012)
  • Author(s): Takumi Yamada
  • Journal Title: Journal of Geometry and Physics Volume: 62 Pages: 740-750
  • Peer Reviewed
• [Journal Article] Ricci flatness of certain compact pseudo-Kahler solvmanifolds (2012)
  • Author(s): Takumi Yamada
  • Journal Title: Journal of Geometry and Physics Volume: 62 Pages: 1338-1345
  • Peer Reviewed
• [Journal Article] n splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature (2012)
  • Author(s): Tetsuya Hosaka
  • Journal Title: Mathematische Zeitschrift Volume: 272 Issue: 3-4 Pages: 1037-1050
  • DOI: 10.1007/s00209-011-0972-x
  • Peer Reviewed
• [Journal Article] On non-sensitive homeomorphisms of the boundary of a proper cocompact CAT(0) space (2011)
  • Author(s): Tetsuya Hosaka
  • Journal Title: The University of Tokyo. Journal of Mathematical Sciences Volume: 18
  • NAID: 120006906073
  • Peer Reviewed
• [Journal Article] On boundaries of Coxeter groups and topological fractal structures (2011)
  • Author(s): Tetsuya Hosaka
  • Journal Title: Tsukuba Journal of Mathematics Volume: 35
  • NAID: 120006312317
  • Peer Reviewed
• [Journal Article] On boundaries of coxeter groups and topological fractal structures (2011)
  • Author(s): Tetsuya Hosaka
  • Journal Title: Tsukuba Journal of Mathematics Volume: 35 Pages: 153-160
  • NAID: 120006312317
  • Peer Reviewed
• [Journal Article] 測度0の鎖回帰集合をもつ写像の通用性について (2011)
  • Author(s): Katsuya Yokoi
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 1728 Pages: 79-83
• [Journal Article] The size of the chain recurrent set for generic maps on an n-dimensional locally (n-1)-connected compact spaces (2010)
  • Author(s): Katsuya Yokoi
  • Journal Title: Colloquium Mathematicum Volume: 119 Pages: 229-236
  • Peer Reviewed
• [Journal Article] Asymptotic Dimension of Proper CAT(0) Spaces that are Homeomorphic to the Plane (2010)
  • Author(s): Naotsugu Chinen and Tetsuya Hosaka
  • Journal Title: Canadian Mathematical Bulletin Volume: 53
  • Peer Reviewed
• [Journal Article] Asymptotic dimension of proper CAT(0) spaces that are homeomorphic to the plane (2010)
  • Author(s): Naotsugu Chinen, Tetsuya Hosaka
  • Journal Title: Canadian Mathematical Bulletin Volume: 53 Pages: 629-638
  • Peer Reviewed
• [Journal Article] Recurrence properties of a class of nonautonomous discrete systems
  • Author(s): Katsuya Yokoi
  • Journal Title: Bulletin of the Belgian Mathematical Society Simon Stevin Volume: (印刷中)
  • Peer Reviewed
• [Journal Article] Reconstructible graphs, simplicial flag complexes of homology manifolds and associated right-angled Coxeter groups
  • Author(s): Tetsuya Hosaka
  • Journal Title: Osaka Journal of Mathematics Volume: (印刷中)
  • NAID: 120005830508
  • Peer Reviewed
• [Journal Article] On a new class of rigid Coxeter group
  • Author(s): Tetsuya Hosaka
  • Journal Title: Hokkaido Mathematical Journal Volume: (印刷中)
  • Peer Reviewed
• [Journal Article] Asymptotic dimension and boundary dimension of proper CAT(0) spaces
  • Author(s): Naotsugu Chinen and Tetsuya Hosaka
  • Journal Title: Tsukuba Journal of Mathematics Volume: (印刷中)
  • NAID: 120006582859
  • Peer Reviewed
• [Journal Article] 無限極限集合に現れる非周期点について～Sarkovskiiの定理より～
  • Author(s): 横井勝弥
  • Journal Title: 京都大学数理解析研究所講究録 Volume: (印刷中)
• [Presentation] 一般化された旗多様体の不変擬ケーラー構造の指数について (2013)
  • Author(s): 山田拓身
  • Organizer: 多様体と幾何構造の融合
  • Place of Presentation: 名城大
  • Year and Date: 2013-03-06
• [Presentation] 一般化された旗多様体の不変擬ケーラー構造の指数について (2013)
  • Author(s): 山田拓身
  • Organizer: 多様体と幾何構造の融合
  • Place of Presentation: 名城大学
• [Presentation] On structure of CAT(0) groups (2012)
  • Author(s): 保坂哲也
  • Organizer: 数理解析研究所研究集会「一般位相幾何学および幾何学的トポロジーの現状と諸問題」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2012-09-27
• [Presentation] Topological fractal structures of boundaries of Coxeter groups and CAT(0) groups (2012)
  • Author(s): 保坂哲也
  • Organizer: 数理解析研究所研究集会「力学系とその周辺分野の研究」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2012-07-11
• [Presentation] On equivariant homeomorphisms of boundaries of CAT(0) groups (2011)
  • Author(s): 保坂哲也
  • Organizer: Rigidity School, Nara 2010/2011
  • Place of Presentation: 奈良商工会議所
  • Year and Date: 2011-03-05
• [Presentation] On equivariant homeomorphisms of boundaries of CAT(0)groups (2011)
  • Author(s): 保坂哲也
  • Organizer: Rigidity School, Nara 2010/2011
  • Place of Presentation: 奈良商工会議所
  • Year and Date: 2011-03-05
• [Presentation] 擬ケーラー多様体上の正則ベクトル場について (2010)
  • Author(s): 山田拓身
  • Organizer: 擬リーマン幾何の展開III
  • Place of Presentation: お茶の水女子大学
  • Year and Date: 2010-12-19
• [Presentation] コンパクト擬ケーラー多様体上の正則ベクトル場について (2010)
  • Author(s): 山田拓身
  • Organizer: 松江微分幾何学研究集会2010
  • Place of Presentation: 島根大学
  • Year and Date: 2010-12-11
• [Presentation] On equivariant homeomorphisms of boundaries of CAT(0) groups (2010)
  • Author(s): 保坂哲也
  • Organizer: 数理解析研究所研究集会「一般位相幾何学及び幾何学的トポロジーの最近の話題とその応用」
  • Place of Presentation: 京都大学 数理解析研究所
  • Year and Date: 2010-10-13
• [Presentation] On equivariant homeomorphisms of boundaries of CAT(0)groups (2010)
  • Author(s): 保坂哲也
  • Organizer: 一般位相幾何学及び幾何学的トポロジーの最近の話題とその応用
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-10-13
• [Presentation] Coxeter群の rank-one isometry とその境界について (2010)
  • Author(s): 保坂哲也
  • Organizer: 第45回位相空間論シンポジウム
  • Place of Presentation: 大阪府立大学 理学部サイエンスホール
  • Year and Date: 2010-06-05
• [Presentation] Coxeter群のrank-one isometryとその境界について (2010)
  • Author(s): 保坂哲也
  • Organizer: 第45回位相空間論シンポジウム
  • Place of Presentation: 大阪府立大学理学部サイエンスホール
  • Year and Date: 2010-06-05