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On statistical properties for nonlinear nonhyperbolic systems

Research Project

Project/Area Number 09640289
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionSapporo University

Principal Investigator

YURI Michiko  Sapporo University, Department of Business Administration, Professor, 経営学部, 教授 (70174836)

Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1998: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1997: ¥1,200,000 (Direct Cost: ¥1,200,000)
KeywordsLarge Deviation / Central limit theorem / Intermittent system / Equilibrium state / Variational principle / Entropy / Nonuniformly hyperbolicity / IntermiHent System / Namuniformly hyperbolicity / indifferent periodic point / Decay of correlations / Perrow-Froberius operator / congormal measure / Variational Principle / Noruniformly hyperbolicity
Research Abstract

(1997)
One of purposes of this project is to establish Large Deviation results for systems without uniformly hyperbolicity. About this problem, I solved it as follows : For piecewise C^1-Bernoulli maps with one indifferent periodicorbits, Large Deviation results for preimages weighted by the derivativeswere established under certain conditions, more precisely, upper boundsin the level 2 Large Deviation Principle <bounded integral>. To solve the problem, Prof.M.Pollicott's visit to Sapporo was meaningful. Further more I could obtain a positive feeling to establish bounds on correlations for nonhyperbolic maps in future. Another purpose of this project is to study asymptotic behavior of ergodic sums, in particuler, convergence to thenormal distributions.About this problem, Prof.M.Denker's visit gave a lot of contributions in solving it. In fact, by his advices I could have a confidenceof importance of my examples and I could establish an extended resultson the central limit theorem which are ajplicable to new nonhyperbolicphenomena. The paper [4] containing the results was submitted to Transaction of the American mathematical Society.
(1998)
In the second year project, I studied the rates of decay ofcorrelationsfor maps with indifferent perodic points. I could present an approach to estimating the rates by generalizing Liverani's random parturbations of Perron-Frobenius operators which goes back to Bunimovich-Sinai-Chernov's Markov approximation method. The result is contained in [5] which is a joint paper with M.Pollicott.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (18 results)

All Other

All Publications (18 results)

  • [Publications] Michiko Yuri: "On the convergence to equilibrium states for certain nonhyperbolic systems" Ergodic Theory and Dynamical Systems. 17. 977-1000 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Michiko Yuri: "Zeta functions for certain nonhyperbolic systems and topological Markov approximations" Ergodic Theory and Dynamical Systems. 18. 1589-1612 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Pollicott, R, Sharp & M.Yuri: "Large Deviations for maps with indifferent periodic points" Nonlinearity. 11. 1173-1184 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Pollicott and M.Yuri: "Dynamical Systems and Ergodic Theory" Cambridge University Press, (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Michiko, Yuri: "On the convergence to equilibrium states for certain nonhyperbolic systems." Ergodic Theory and Dynamical Systems. 17. 977-1000 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Michiko, Yuri: "Zeta functions for certain nonhyperbolic systems and topological Markov approximations." Ergodic Theory and Dynamical Systems. 18. 1589-1612 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Pollicott R.Sharp &M.Yuri: "Large Deviations for maps with indifferent periodic points" Nonlinearity. 11. 1173-1184 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Yuri: "Statistical properties for nonhyperbolic maps with finite range structure" (Preprint.).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Pollicott&M.Yuri: "Statistical properties of maps with indifferent periodic points." (Preprint.).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Pollicottand M.Yuri: Dynamical Systems and Ergodic Theory. Cambridge University Press, (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Michiko Yuri: "Zeta functions for certain nonhyperbolic systems and topological Marker approximations" Ergodic Theory and Dynamical Systems. 18. 1589-1612 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Michiko Yuri(with M.Pollicott & R.Sharp): "Lange Deriations for maps with indifferent periodic points" Nonlirearity. 11. 1173-1184 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Michiko Yuri: "Thermodynamic Formalism for certain nonlyperbolic maps" Ergodic Theory and Dynamical Systems. (印刷中)発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] Michiko Yuri(with M.Pollicott): "Dynamical Systems and Ergodic Theory" Cambridge University Press, 179 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Michiko Yuri: "On the convergence to equilibrium states for certain nonlyperbolic Systems" Ergodic Theory and Dynamical Systems. 17. 977-1000 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Michiko Yuri: "3eta functions for certain nonlyperbolic systems and topological Markou approximation" Ergodic Theory and Dynamical Systems. (印刷中).

    • Related Report
      1997 Annual Research Report
  • [Publications] M. Pollicott, R. Sharp & M. Yuri: "Large Deviations for maps with indifferent Periodic points" Nonlinearity. (印刷中).

    • Related Report
      1997 Annual Research Report
  • [Publications] M. Yuri & M. Pollicott: "Dynamical Systems and Ergodic Theory" Cambridge University Press, 179 (1998)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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