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Large deviation principle and multifractal analysis in dynamical systems

Research Project

Project/Area Number 24540212
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Global analysis
Research InstitutionHiroshima University

Principal Investigator

Chung Yong Moo  広島大学, 工学(系)研究科(研究院), 准教授 (20314734)

Co-Investigator(Renkei-kenkyūsha) TAKAHASI Hiroki  慶應義塾大学, 理工学部, 准教授 (00467440)
SUMI Naoya  熊本大学, 自然科学研究科, 教授 (50301411)
MIKAMI Toshio  津田塾大学, 学芸学部, 教授 (70229657)
Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords力学系 / 大偏差原理 / マルチフラクタル / 可微分力学系 / マルチフラクタル解析 / 力学系理論
Outline of Final Research Achievements

We obtained a criterion to hold the large deviation principle for smooth dynamical systems on the interval. If a multimodal map without flat critical points has the following properties: (1) the exponential growth of the derivative on the set of critical values with respect to the time evolution; (2) the sub-exponential slow recurrence of the critical orbits; (3) the topological exactness, the large deviation principle of level 2 holds. From our result it is shown that almost every stochastic quadratic map satisfies the large deviation principle. Moreover we gave a representation of the Birkhoff spectrum by using thermodynamic formalism, and showed its continuity.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report

Research Products

(40 results)

All 2016 2015 2014 2013 2012 Other

All Journal Article Presentation Remarks

  • [Journal Article] Partial hyperbolicity and specification2016

    • Author(s)
      鷲見直哉,山本謙一郎,P.Varandas
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 144 Pages: 1161-1170

    • DOI

      10.1090/proc/12830

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Equilibrium measures at temperature zero for Henon-like maps at the first bifurcation2016

    • Author(s)
      Hiroki Takahasi
    • Journal Title

      SIAM Journal on Applied Dynamical Systems

      Volume: 15 Pages: 106-124

    • DOI

      10.1137/15m1015741

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Equilibrium measures for the Henon map at the first bifurcation: uniqueness and geometric/statistical properties2016

    • Author(s)
      Senti, Samuel; Takahasi, Hiroki
    • Journal Title

      Ergodic Theory and Dynamical Systems

      Volume: 36 Pages: 215-255

    • DOI

      10.1017/etds.2014.61

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Birkhoff spectrum for Henon-like maps at the first bifurcation2016

    • Author(s)
      Hiroki Takahasi
    • Journal Title

      Dynamical Systems: An International Journal

      Volume: 31 Pages: 41-59

    • DOI

      10.1080/14689367.2015.1102201

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] 2次写像力学系の統計的性質2015

    • Author(s)
      鄭 容武
    • Journal Title

      数理科学

      Volume: 626-8 Pages: 20-25

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Specification and partial hyperbolicity for flows2015

    • Author(s)
      鷲見直哉,山本謙一郎,P.Varandas
    • Journal Title

      Dynamical Systems: An International Journal

      Volume: 30 Pages: 501-524

    • DOI

      10.1080/14689367.2015.1081380

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Two end points marginal problem by stochastic optimal transportation2015

    • Author(s)
      Toshio Mikami
    • Journal Title

      SIAM Journal on Control and Optimization

      Volume: 53 Pages: 2449-2461

    • DOI

      10.1137/14099070x

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multifractal formalism for Benedicks-Carleson quadratic maps2014

    • Author(s)
      Yong Moo Chung and Hiroki Takahasi
    • Journal Title

      Ergodic Theory and Dynamical Systems

      Volume: published online Pages: 1116-1141

    • DOI

      10.1017/etds.2012.188

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] カオス的な2次写像力学系のマルチフラクタル解析2013

    • Author(s)
      鄭 容武
    • Journal Title

      数理解析研究所講究録

      Volume: 1855 Pages: 56-57

    • Related Report
      2013 Research-status Report
  • [Journal Article] Large deviation principle for Benedicks-Carleson quadratic maps2012

    • Author(s)
      Yong Moo Chung, Hiroki Takahasi
    • Journal Title

      Communications in Mathematical Physics

      Volume: 315 Pages: 803-826

    • DOI

      10.1007/s00220-012-1540-x

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] 区間力学系の大偏差原理について2016

    • Author(s)
      鄭 容武;高橋 博樹;Juan Rivera-Letelier
    • Organizer
      日本数学会年会
    • Place of Presentation
      筑波大学
    • Year and Date
      2016-03-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] Universality of the large deviation principle in one-dimensional dynamics2016

    • Author(s)
      Yong Moo CHUNG
    • Organizer
      Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
    • Place of Presentation
      Brown University, Providence, RI, USA
    • Year and Date
      2016-03-09
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 可微分力学系の大偏差原理について2016

    • Author(s)
      鄭 容武
    • Organizer
      広島・岡山解析確率論セミナー
    • Place of Presentation
      広島大学
    • Year and Date
      2016-02-22
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] 確率最適輸送問題とその関連する話題について2016

    • Author(s)
      三上 敏夫
    • Organizer
      広島・岡山解析確率論セミナー
    • Place of Presentation
      広島大学
    • Year and Date
      2016-02-22
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Removable of the phase transition of 1-2x^2 on [-1, 1] and theormodynamics of the Henon map at the first bifurcation2016

    • Author(s)
      高橋 博樹
    • Organizer
      冬の力学系研究集会
    • Place of Presentation
      日本大学軽井沢研修所
    • Year and Date
      2016-01-11
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] 多峰写像力学系の大偏差原理とその普遍性2016

    • Author(s)
      鄭 容武
    • Organizer
      冬の力学系研究集会
    • Place of Presentation
      日本大学軽井沢研修所
    • Year and Date
      2016-01-10
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] 低次元力学系におけるSRB測度の一意性について2016

    • Author(s)
      鷲見 直哉
    • Organizer
      冬の力学系研究集会
    • Place of Presentation
      日本大学軽井沢研修所
    • Year and Date
      2016-01-10
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] On the uniqueness of Sinai-Ruelle-Bowen measures for low-dimensional dynamical systems2015

    • Author(s)
      Naoya SUMI
    • Organizer
      Sino-Japanese Workshop on Dynamic Systems and Fractals
    • Place of Presentation
      Yinyuan Hotel, Ningbo, China
    • Year and Date
      2015-12-27
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 区間力学系における大偏差原理の普遍性について2015

    • Author(s)
      鄭 容武
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      岡山大学
    • Year and Date
      2015-12-16
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Escape rate for nonhyperbolic one-dimensional maps2015

    • Author(s)
      高橋 博樹
    • Organizer
      大自由度分子系における化学反応機序の理解と制御
    • Place of Presentation
      北海道大学
    • Year and Date
      2015-10-31
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] 一次元力学系の大偏差原理とその普遍性について2015

    • Author(s)
      高橋 博樹
    • Organizer
      京都力学系セミナー
    • Place of Presentation
      京都大学
    • Year and Date
      2015-10-16
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] 区間力学系の大偏差原理2015

    • Author(s)
      鄭 容武
    • Organizer
      Hiroshima Dynamics Day 2015
    • Place of Presentation
      広島大学
    • Year and Date
      2015-10-09
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Large deviation principle and its universality in one-dimensional dynamics2015

    • Author(s)
      高橋 博樹
    • Organizer
      関東力学系セミナー
    • Place of Presentation
      東京大学
    • Year and Date
      2015-09-25
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Lyapunov spectrum for Henon-like maps at the first bifurcation2015

    • Author(s)
      Hiroki TAKAHASI
    • Organizer
      School and Conference in Dynamical Systems
    • Place of Presentation
      ICTP, Trieste, Italy
    • Year and Date
      2015-08-04
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] ある非一様双曲的一次元写像の逃げ率公式について2015

    • Author(s)
      高橋 博樹
    • Organizer
      力学系とその諸分野への応用
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-07-01
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Sufficient conditions for the uniqueness of Sinai-Ruelle-Bowen measures2015

    • Author(s)
      Naoya SUMI
    • Organizer
      The Workshop on Measurable and Topological Dynamical Systems
    • Place of Presentation
      NIMS, Daejeon, South Korea
    • Year and Date
      2015-06-30
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Escape rate formula for some non-uniformly hyperbolic one-dimensional maps2015

    • Author(s)
      Hiroki TAKAHASI
    • Organizer
      NCTS Workshop on Dynamical Systems
    • Place of Presentation
      NCTS, Taipei, Taiwan
    • Year and Date
      2015-05-22
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Large deviation principle for one-dimensional maps under weak hyperbolicity assumptions2015

    • Author(s)
      Hiroki TAKAHASI
    • Organizer
      IMS XXV, Celebrating 25 years of low-dimensional dynamics
    • Place of Presentation
      Stony Brook University, New York, NY, USA
    • Year and Date
      2015-05-10
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A conjecture on large deviations principle for stadium billiards2015

    • Author(s)
      鄭 容武
    • Organizer
      Keio Dynamics Days 2015
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2015-03-04
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Large deviation principle for multimodal maps with weak hyperbolicity2014

    • Author(s)
      Yong Moo Chung
    • Organizer
      Limit theorems in dynamics and applications
    • Place of Presentation
      CIRM, Marseille, France
    • Year and Date
      2014-07-07
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Large deviation principle for chaotic dynamical systems

    • Author(s)
      Yong Moo Chung
    • Organizer
      The Second Pacific Rim Mathematical Association Congress
    • Place of Presentation
      上海交通大学(中国)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Large deviation principle for interval maps with weak hyperbolicity

    • Author(s)
      Yong Moo Chung
    • Organizer
      Measurable and Topological Dynamical Systems
    • Place of Presentation
      慶應義塾大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 弱い双曲性をもつ多峰写像力学系の大偏差原理

    • Author(s)
      鄭 容武
    • Organizer
      2013年度冬の力学系研究集会
    • Place of Presentation
      広島大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 非一様双曲型力学系の大偏差原理

    • Author(s)
      鄭 容武
    • Organizer
      非線形・非平衡系シンポジウムII -複雑系とエルゴード理論-
    • Place of Presentation
      早稲田大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Multifractal formalism for Benedicks-Carleson quadratic maps

    • Author(s)
      Yong Moo Chung
    • Organizer
      School and Conference in Dynamical Systems
    • Place of Presentation
      ICTP, Trieste, Italy
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] ある2次写像力学系のマルチフラクタル解析

    • Author(s)
      鄭 容武
    • Organizer
      研究集会「力学系とその周辺分野の研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] カオス的な2次写像力学系のマルチフラクタル解析

    • Author(s)
      鄭 容武
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 2次写像力学系の Lebesgue 測度に関する大偏差原理

    • Author(s)
      鄭 容武
    • Organizer
      冬の力学系研究集会
    • Place of Presentation
      日本大学軽井沢研修所
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Markov towers and large deviation principle

    • Author(s)
      Yong Moo Chung
    • Organizer
      Large deviations and thermodynamical formalism
    • Place of Presentation
      EPFL, Lausanne, Switzerland
    • Related Report
      2012 Research-status Report
    • Invited
  • [Remarks] 広島大学大学院工学研究院電気電子システム数理部門数理学研究室

    • URL

      http://home.hiroshima-u.ac.jp/amath/mathlab/?FrontPage

    • Related Report
      2015 Annual Research Report

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Published: 2013-05-31   Modified: 2019-07-29  

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