Analytic properties of dynamical zeta functions and stable ergodicity

• Project/Area Number: 19840038
• Research Category: Grant-in-Aid for Young Scientists (Start-up)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Kyushu Institute of Technology (2008); Kyushu University (2007)
• Principal Investigator: HIRAYAMA Michihiro Kyushu Institute of Technology, 工学研究院, 准教授 (50452735)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,105,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥405,000); Fiscal Year 2008: ¥1,755,000 (Direct Cost: ¥1,350,000、Indirect Cost: ¥405,000); Fiscal Year 2007: ¥1,350,000 (Direct Cost: ¥1,350,000)
• Keywords: 安定エルゴード性 / ハウスドルフ次元

Research Abstract

相空間の標準的な測度を保つ写像が与えられると, その測度に依存したエルゴード的鉢と呼ばれる集合が定義できる. エルゴード的な系であればこの集合は全測度をもち, 従って特に空でない. しかしながら一般に, エルゴード的でない系についてエルゴード的鉢が空でないのか否かは非自明な問題である. 本研究では, 適当な条件の下で, エルゴード的鉢のHausdorff 次元の評価を与えた. この結果から特に, エルゴード的鉢は空でないことが従う.

Research Products

• [Journal Article] Absolutely continuous invariant measures for expansive diffeomorphisms of the 2-torus (2007)
  • Author(s): Michihiro Hirayama and Naoya Sumi
  • Journal Title: Hiroshima Mathematical Journal vol.37 Pages: 491-517
  • NAID: 110006455964
  • Peer Reviewed
• [Journal Article] Non- absolutely continuous foliations (2007)
  • Author(s): Michihiro Hirayama and Yakov Pesin
  • Journal Title: Israel Journal of Mathematics vol.160 Pages: 173-187
  • Peer Reviewed
• [Journal Article] Non-absolutely continuous foliations (2007)
  • Author(s): Michihiro Hirayama, et. al.
  • Journal Title: Israel Journal of Mathematics 160 Pages: 173-187
  • Peer Reviewed
• [Journal Article] Absolutely continuous invariant measures for expansive diffeomorphisms of the 2-torus (2007)
  • Author(s): Michihiro Hirayama, et. al.
  • Journal Title: 数理解析研究所講究録 1552 Pages: 22-26
  • NAID: 110006455964
• [Journal Article] Absolutely continuous invarant measures for expansive diffeomorphisms of the 2-torus (2007)
  • Author(s): Michihiro Hirayama, et. al.
  • Journal Title: Hiroshima Mathematical Journal 37 Pages: 491-517
  • Peer Reviewed
• [Presentation] Hausdorff dimension of the generic set (2008)
  • Author(s): Michihiro Hirayama
  • Organizer: エルゴート理論小研究集会
  • Place of Presentation: 九州大学
  • Year and Date: 2008-06-16
• [Presentation] Absolutely continuous invariant measures for expansive diffeomorphisms of the 2-torus (2007)
  • Author(s): Michihiro Hirayama
  • Organizer: COE Conference on the Development of Dynamic Mathematics with High Functionality 2007
  • Year and Date: 2007-10-03