An analysis of dissipative phenomena and intermittency in complex systems via a generalized variational principle

• Project/Area Number: 19540109
• 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: Hokkaido University
• Principal Investigator: YURI Michiko Hokkaido University, 大学院・理学研究院, 教授 (70174836)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2008: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000); Fiscal Year 2007: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
• Keywords: Dissipative phenomena / Intermittency / Phase transition / Variational principle / Weak Gibbs measure / Nonhyperbolicity / Equilibrium state / Irreversibility / Variational Principle / Non-hynerbolicity / Non-hyperbolicity

Research Abstract

Sofic条件を満たす可算生成分割を保持する非可逆離散写像に対し、非特異測度に関するtransfer operatorを介在しエントロピー生成の時間発展の漸近平均を捉え、この量が消滅する事が、両側非特異測度に関する一般化されたエントロピーにどのような影響を与えるかを明らかにした。更にindifferent periodic pointを持つ時、絶対連続な不変確率測度に関する時間相関関数の減少のオーダーが多項式的である事を、indifferent periodic pointの近傍の測度減少のオーダーが劣指数的となる事と関連付け証明した。

Research Products

• [Journal Article] Entropy production at weak Gibbs measures and a generalized variational principle (2009)
  • Author(s): Michiko Yuri
  • Journal Title: Ergodic Theory and Dynamical systems (to appear)
  • NAID: 120001469142
  • Peer Reviewed
• [Journal Article] Entropy production at weak Gibbs measures and a generalized variational principle (2009)
  • Author(s): Michiko Yuri
  • Journal Title: Ergodic Theory and Dynamical Systems (to appear)
  • NAID: 120001469142
  • Peer Reviewed
• [Journal Article] Polynomial decay of correlations for intermittent sofic systems (2008)
  • Author(s): Michiko Yuri
  • Journal Title: Discrete and Continuous dynamical systems 22 Pages: 445-464
  • Peer Reviewed
• [Journal Article] Polynomial decay of correlations for intermittent sofic systems (2008)
  • Author(s): Michiko Yuri
  • Journal Title: Discrete and Continuous Dynamical Systems 22 Pages: 445-464
  • Peer Reviewed
• [Journal Article] Polynomial decay of correlations for intermittent sofic systems (2008)
  • Author(s): Michiko Yuri
  • Journal Title: Discrete and Continuous Dynamical Systems(to appear)
  • Peer Reviewed
• [Presentation] A generalized variational principle for non-stationary process and a realization of the infinite past (2008)
  • Author(s): Michiko Yuri
  • Organizer: Dynamics of complex systems 2008
  • Place of Presentation: 北海道大学遠友学舎
  • Year and Date: 2008-09-02
• [Presentation] Polynomial decay of correlations for intermittent sofic systems (2007)
  • Author(s): Michiko Yuri
  • Organizer: エルゴード理論とその応用
  • Place of Presentation: 慶應義塾大学日吉キャンパス
  • Year and Date: 2007-12-20
• [Presentation] Polynomial Decay of correlations for intermittent sofic systems (2007)
  • Author(s): Michiko Yuri
  • Organizer: エルゴード理論とその応用
  • Place of Presentation: 慶應義塾大学日吉キャンパス
  • Year and Date: 2007-12-20
• [Presentation] Entropy production at weak Gibbs measures and a generalized variational principle (2007)
  • Author(s): Michiko Yuri
  • Organizer: Nonuniformly Hyperbolic Dynamics and Smooth Ergodic Theory
  • Place of Presentation: Institute Superior Tecnico, Lisbon, PORTUGAL
  • Year and Date: 2007-06-28
• [Presentation] Entropy production at weak Gibbs measures and a generalized variational principle (2007)
  • Author(s): Michiko Yuri
  • Organizer: Nonuniformly Hyperbolic Dynamics and Smooth Ergodic Theory
  • Place of Presentation: Institute Superior Tecnico, Lisbon, Portugal
  • Year and Date: 2007-06-28