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Study of large deviation principle by the classification of finite orbits

Research Project

Project/Area Number 16K17611
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionNagaoka University of Technology

Principal Investigator

Yamamoto Kenichiro  長岡技術科学大学, 工学研究科, 講師 (30635181)

Project Period (FY) 2016-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords大偏差原理 / 明記性 / 記号力学系 / 公理A力学系 / 非双曲型力学系 / 部分双曲型力学系 / 一方通行の明記性 / 有限軌道の分類
Outline of Final Research Achievements

In this research project, we consider a large deviation principle for systems without the specification property. In particular, we introduce a weaker form of the specification property, called the one-way specification property, which holds for some typical Axiom A diffeomorphisms and sofic minus-beta-shifts.
We also introduce criteria for systems with this property to satisfy the large deviation principle. As an application, we show that these three examples satisfy a large deviation principle with the normalized Lebesgue measure.

Report

(3 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • Research Products

    (10 results)

All 2018 2017 2016

All Journal Article (2 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 2 results,  Acknowledgement Compliant: 1 results) Presentation (8 results) (of which Int'l Joint Research: 2 results)

  • [Journal Article] Large deviations for systems with non-uniform structure2017

    • Author(s)
      Vaughn Climenhaga, Daniel J. Thompson, Kenichiro Yamamoto
    • Journal Title

      Transactions of the American Mathematical Society

      Volume: 369 Issue: 6 Pages: 4167-4192

    • DOI

      10.1090/tran/6786

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On the one-way specification property and large deviations for systems with non-dense ergodic measures2017

    • Author(s)
      Kenichiro Yamamoto
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 印刷中

    • NAID

      130007411754

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Large deviations for systems with non-dense ergodic measures2018

    • Author(s)
      山本謙一郎
    • Organizer
      Workshop「数論とエルゴード理論」
    • Related Report
      2017 Annual Research Report
  • [Presentation] Global large deviations for classical Axiom A diffeomorphisms2017

    • Author(s)
      山本謙一郎
    • Organizer
      RIMS 共同研究 力学系-理論と応用の連携探索
    • Related Report
      2017 Annual Research Report
  • [Presentation] On the one-way specification property and large deviations for systems with non-dense ergodic measures2017

    • Author(s)
      山本謙一郎
    • Organizer
      Workshop on Dynamical Systems 2017
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On the one-way specification property and large deviations for systems with non-dense ergodic measures2017

    • Author(s)
      山本謙一郎
    • Organizer
      エルゴード理論とその周辺
    • Related Report
      2017 Annual Research Report
  • [Presentation] On the one-way specification property and large deviations for non-transitive systems2017

    • Author(s)
      山本謙一郎
    • Organizer
      2016年度冬の力学系研究集会
    • Place of Presentation
      日本大学軽井沢研修所
    • Related Report
      2016 Research-status Report
  • [Presentation] Large deviations for systems whose ergodic measures are not entropy-dense2016

    • Author(s)
      山本謙一郎
    • Organizer
      2016年度RIMS研究集会-力学系とその関連分野の連携探索
    • Place of Presentation
      京都大学
    • Related Report
      2016 Research-status Report
  • [Presentation] On the one-way specification property and its applications2016

    • Author(s)
      山本謙一郎
    • Organizer
      関東力学系セミナー
    • Place of Presentation
      東京大学
    • Related Report
      2016 Research-status Report
  • [Presentation] Large deviations beyond specification2016

    • Author(s)
      山本謙一郎
    • Organizer
      Advances in Ergodic Theory, Hyperbolic Dynamics and Statistical Laws
    • Place of Presentation
      The Australoian National University
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research

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Published: 2016-04-21   Modified: 2019-03-29  

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