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Relation between hyperbolic structure of partially hyperbolic systems and ergodic limit theorems

Research Project

Project/Area Number 23740136
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Global analysis
Research InstitutionTokyo National College of Technology

Principal Investigator

HATOMOTO Jin  東京工業高等専門学校, 一般教育科, 准教授 (70547801)

Project Period (FY) 2011 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥260,000 (Direct Cost: ¥200,000、Indirect Cost: ¥60,000)
Fiscal Year 2012: ¥130,000 (Direct Cost: ¥100,000、Indirect Cost: ¥30,000)
Fiscal Year 2011: ¥130,000 (Direct Cost: ¥100,000、Indirect Cost: ¥30,000)
Keywords部分双曲系 / 弱双曲積構造 / SRB 測度 / 時間相関関数の多項式的減衰 / SRB測度 / オールモースト・アノソフ系 / 双曲積構造 / 相関関数の減衰 / 中心極限定理(CLT) / 大偏差原理(LDP)
Research Abstract

We dealt with discrete time dynamical systems with weak hyperbolic product structure. We established polynomial upper bounds on large deviations for such dynamical systems associated with its Sinai-Ruelle-Bowen(SRB) measure if the return tail of the weak hyperbolic product structure decays polynomially. Applications of our results are some almost Anosov diffeomorphisms with uniformly contracting direction of which restriction on one dimensional center unstable direction behaves as a Manneville-Pomeau map.

Report

(3 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Research-status Report
  • Research Products

    (5 results)

All 2012

All Journal Article (4 results) (of which Peer Reviewed: 2 results) Book (1 results)

  • [Journal Article] Polynomial upper bounds on large and moderate deviations for diffeomorphisms with weak hyperbolic product structure2012

    • Author(s)
      Jin Hatomoto
    • Journal Title

      Far East J Math Sci.

      Volume: 69(1) Pages: 1-25

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] 弱双曲積構造をもつ微分 同相写像に対する大偏差原理の上限評価2012

    • Author(s)
      波止元仁
    • Journal Title

      東京工業高等専門学校研究報告書

      Volume: 第43号 Pages: 51-57

    • NAID

      40019343704

    • Related Report
      2012 Final Research Report
  • [Journal Article] Polynomial upper bounds on large and moderate deviations for diffeomorphisms with weak hyperbolic product structure2012

    • Author(s)
      Jin Hatomoto
    • Journal Title

      Far East Journal of Mathematical Sciences

      Volume: 69 Pages: 1-25

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 弱双曲積構造をもつ微分同相写像に対する大偏差原理の上限評価2012

    • Author(s)
      波止元 仁
    • Journal Title

      東京工業高等専門学校研究報告書

      Volume: 第43号 Pages: 51-57

    • NAID

      40019343704

    • Related Report
      2012 Annual Research Report
  • [Book] Upper bounds on large deviation for diffeomorphisms with weak hyperbolic product structure2012

    • Author(s)
      Jin Hatomoto
    • Total Pages
      9
    • Publisher
      Reserch report of Tokyo National College of Technology
    • Related Report
      2011 Research-status Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

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