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Shibayama, Mitsuru

Graduate School of Informatics, Department of Applied Mathematics and Physics Associate Professor

Shibayama, Mitsuru
list
    Last Updated :2022/05/14

    Basic Information

    Faculty

    • 工学部

    Professional Memberships

    • The Mathematical Society of Japan

    Academic Degree

    • 修士(理学)(京都大学)
    • 博士(理学)(京都大学)

    Academic Resume (Graduate Schools)

    • 京都大学, 大学院理学研究科修士課程数学・数理解析専攻, 修了
    • 京都大学, 大学院理学研究科博士後期課程数学・数理解析専攻, 修了

    Academic Resume (Undergraduate School/Majors)

    • 京都大学, 理学部, 卒業

    Research History

    • From 01 Jul. 2015
      Kyoto University, Associate Professor
    • From 01 Apr. 2011
      Osaka University, Associate Professor
    • Kyoto University

    Profile

    • Profile

      His fields of interest are dynamical systems theory and variational problems.

    Language of Instruction

    • English

    ID,URL

    Website(s) (URL(s))

    researchmap URL

    list
      Last Updated :2022/05/14

      Research

      Research Topics, Overview of the research

      • Research Topics

        Hamiltonian dynamical systems, variational problems and celestial mechanics.
      • Overview of the research

        Hamiltonian dynamical systems, variational problems and celestial mechanics.

      Research Interests

      • Variational problems
      • Celestial mechanics
      • Dynamical systems

      Research Areas

      • Natural sciences, Mathematical analysis

      Papers

      • Variational existence proof for multiple periodic orbits in the planar circular restricted three-body problem
        Yuika Kajihara; Mitsuru Shibayama
        Nonlinearity, 03 Mar. 2022
      • Nonintegrability of the Reduced Planar Three-body Problem with Generalized Force
        Mitsuru Shibayama; Junji Yamada
        Regular and Chaotic Dynamics, Jul. 2021, Peer-reviewed
      • ポテンシャル系の変分解析と周期解の安定性,
        柴山允瑠
        応用数理, 2020, Peer-reviewed, Invited
      • Variational proof of the existence of brake orbits in the planar 2-center problem
        Yuika Kajihara; Mitsuru Shibayama
        Discrete and Continuous Dynamical Systems-A, Oct. 2019, Peer-reviewed
      • Variational Construction of Orbits Realizing Symbolic Sequences in the Planar Sitnikov Problem
        Mitsuru Shibayama
        Regular and Chaotic Dynamics, 2019, Peer-reviewed
      • Non-integrability of the spacial n-center problem
        Mitsuru Shibayama
        Journal of Differential Equations, 15 Sep. 2018, Peer-reviewed
      • Linear stability of periodic three-body orbits with zero angular momentum and topological dependence of Kepler's third law: a numerical test
        V Dmitrašinović; Ana Hudomal; Mitsuru Shibayama; Ayumu Sugita
        Journal of Physics A: Mathematical and Theoretical, Aug. 2018, Peer-reviewed
      • PERIODIC SOLUTIONS FOR A PRESCRIBED-ENERGY PROBLEM OF SINGULAR HAMILTONIAN SYSTEMS
        Mitsuru Shibayama
        DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, May 2017, Peer-reviewed
      • Three topologically nontrivial choreographic motions of three bodies
        Milovan Suvakov; Mitsuru Shibayama
        CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, Feb. 2016, Peer-reviewed
      • NON-INTEGRABILITY CRITERION FOR HOMOGENEOUS HAMILTONIAN SYSTEMS VIA BLOWING-UP TECHNIQUE OF SINGULARITIES
        Mitsuru Shibayama
        DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, Aug. 2015, Peer-reviewed
      • Minimax approach to the n-body problem
        Mitsuru Shibayama
        NONLINEAR DYNAMICS IN PARTIAL DIFFERENTIAL EQUATIONS, 2015, Peer-reviewed
      • Variational Proof of the Existence of the Super-Eight Orbit in the Four-Body Problem
        Mitsuru Shibayama
        ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, Oct. 2014, Peer-reviewed
      • Families of symmetric relative periodic orbits originating from the circular Euler solution in the isosceles three-body problem
        Mitsuru Shibayama; Kazuyuki Yagasaki
        CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, May 2011, Peer-reviewed
      • NON-INTEGRABILITY OF THE COLLINEAR THREE-BODY PROBLEM
        Mitsuru Shibayama
        DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, May 2011, Peer-reviewed
      • Minimizing Periodic Orbits with Regularizable Collisions in the n-Body Problem
        Mitsuru Shibayama
        ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, Mar. 2011, Peer-reviewed
      • Heteroclinic connections between triple collisions and relative periodic orbits in the isosceles three-body problem
        Mitsuru Shibayama; Kazuyuki Yagasaki
        NONLINEARITY, Oct. 2009, Peer-reviewed
      • Free-fall and heteroclinic orbits to triple collisions in the isosceles three-body problem
        Mitsuru Shibayama
        JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 2009, Peer-reviewed
      • Existence and stability of periodic solutions in the isosceles three-body problem
        Mitsuru Shibayama
        RIMS Kˆokyuˆroku Bessatsu, 2009, Peer-reviewed
      • Multiple symmetric periodic solutions to the 2n-body problem with equal masses
        Mitsuru Shibayama
        NONLINEARITY, Oct. 2006, Peer-reviewed

      Misc.

      • Variational analysis for a prescribed-energy problem via the action functional(Problems on mathematical science and new development in the theory of dynamical systems)
        Mitsuru Shibayama
        RIMS Kôkyûroku, Apr. 2021
      • A variational proof of the existence of periodic orbits in the anisotropic Kepler problem(Problems on mathematical science and new development in the theory of dynamical systems)
        Shota Iguchi; Mitsuru Shibayama
        RIMS Kôkyûroku, Apr. 2021
      • Variational analysis for periodic points of the area-preserving Henon map and the relation between the Morse indices and the bifurcations(Problems on mathematical science and new development in the theory of dynamical systems)
        Mitsuru Shibayama; Mitsutaka Yamada
        RIMS Kôkyûroku, Apr. 2021
      • 天体力学と数学 (特集 物理学における数学的発想 : なぜ数学の考え方が必要になるか)
        柴山 允瑠
        数理科学, Apr. 2016
      • ケプラー型ポテンシャル系のエネルギー固定問題における周期解 (実領域における常微分方程式の定性的研究)
        柴山 允瑠
        数理解析研究所講究録, Apr. 2016
      • ハミルトン系の非可積分性の証明 (力学系の作る集団ダイナミクス : 保存系・散逸系の枠組みを越えて)
        柴山 允瑠
        数理解析研究所講究録, Mar. 2013
      • 変分法による軌道の探索
        柴山允瑠
        自動制御連合講演会(CD-ROM), 2013
      • 最急降下法による探査機の軌道設計
        柴山允瑠
        天体力学N体力学研究会集録(CD-ROM), 2012
      • 二等辺三体問題の三体衝突間のヘテロクリニック軌道と相対周期軌道 (幾何学的力学系理論とその周辺)
        柴山 允瑠; 矢ヶ崎 一幸
        数理解析研究所講究録, Jun. 2010
      • 舞踏解に関する第二変分の数値計算
        柴山允瑠
        天体力学N体力学研究会集録(CD-ROM), 2010
      • 3体問題の衝突特異点が正則化可能となる場合に関する考察
        柴山允瑠
        天体力学N体力学研究会集録, Jan. 2010
      • 3体問題の振動解
        柴山允瑠
        天体力学N体力学研究会集録, 2006

      Presentations

      • Periodic solutions of a prescribed-energy problem for a singular Hamiltonian system
        Mitsuru Shibayama
        The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Hyatt Regency Orlando, Florida, USA, Jul. 2016, American Institute of Mathematical Science, Invited
      • n体問題の周期軌道の変分解析
        Mitsuru Shibayama
        日本数学会2016年度年会函数方程式分科会, 筑波大学, Mar. 2016, 日本数学会, Invited
      • Non-integrability criterion for homogeneous Hamiltonian systems via blowing-up technique of singularities
        Mitsuru Shibayama
        The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Madrid, Spain, Jul. 2014, American Institute of Mathematical Science, Invited
      • Variational proof of the existence of the super-eight orbit in the four-body problem
        Mitsuru Shibayama
        The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Universidad Autónoma de Madrid, Madrid, Spain, Jul. 2014, American Institute of Mathematical Science, Invited
      • Variational proof of the existence of the super-eight orbit in the four-body problem
        Mitsuru Shibayama
        The Asian Mathematical Conference 2013, BEXCO, Busan, Kore, Jun. 2013, Korean Mathematical Society, Southeast Asian Mathematical Society, Invited
      • Non-integrability criterion for homogeneous Hamiltonian systems via blowing-up theory of singularities
        Mitsuru Shibayama
        New Perspectives on the N-body Problem, BIRS, Banff, Canada, Jan. 2013, Invited
      • 斉次ハミルトン系の特異点のブローアップと可積分性の判定
        Mitsuru Shibayama
        数理解析研究所共同研究集会 力学系の作る集団ダイナミクス: 保存系・散逸系の枠組みを越えて, 京都大学数理解析研究所, Sep. 2012, Invited
      • Non-integrability criterion for homogeneous Hamiltonian systems via blowing-up theory of singularities
        Mitsuru Shibayama
        Workshop on Variational Methods in N-Body and Vortex Dynamics, Università del Salento, Lecce, Italy, Jun. 2012, Invited
      • Variational approach to the n-body problem
        Mitsuru Shibayama
        Sino-Japan Conference of Young Mathematicians, Nankai University, Tianjin, China, Dec. 2011, Invited
      • A variational proof of the existence of Gerver's super-eight orbit in the four-body problem
        Mitsuru Shibayama
        2nd UPC Integrability Seminar, Universitat Politècnica de Catalunya, Barcelona, Spain, Jun. 2010, Invited
      • 変分法による周期解の存在証明
        Mitsuru Shibayama
        天体力学N体力学研究会, 木更津工業高等専門学校, Mar. 2007, Invited

      Books and Other Publications

      • ハミルトン力学系
        柴山 允瑠, Single work
        サイエンス社, Dec. 2016, Not refereed

      Media Coverage

      • 古典力学とポテンシャル
        数理科学, Mar. 2022
      • 三体問題に進展 周期解に新たな予想(R. モンゴメリー著,柴山訳)
        日経サイエンス, Mar. 2020
      • ハミルトンの最小作用の原理
        数学セミナー, Sep. 2016
      • 天体力学と数学
        数理科学, Apr. 2016
      • 古典力学における線形と非線形
        数理科学, Nov. 2011
      • 書評「天体力学のパイオニアたち」
        数学通信, Feb. 2010
      • 3体問題
        数学セミナー, Jul. 2009

      External funds: Kakenhi

      • 変分法による周期軌道の個数評価と分岐解析および複雑な軌道の存在証明
        Grant-in-Aid for Scientific Research (C)
        Basic Section 12020:Mathematical analysis-related
        Kyoto University
        柴山 允瑠
        From 01 Apr. 2018, To 31 Mar. 2023, Granted
        面積保存写像;天体力学;Arnold拡散;Kirkwood gaps;変分法;モース理論;衛星形成;分岐;3体問題;不変集合;シンプレクティック写像;サドル-センター;ポテンシャル系;共鳴;周期軌道;変分問題;安定性
      • 標準形理論による可積分系の剛性と大域構造の解析
        Grant-in-Aid for Scientific Research (C)
        Kanagawa University;Tokyo Metropolitan University;Kanazawa University
        伊藤 秀一
        From 01 Apr. 2016, To 31 Mar. 2020, Granted
        ハミルトン力学系;超可積分系;バーコフ標準形;写像の標準形;可積分系;剛性;バーコフ標準化;標準形理論;シンプレクティック写像;非可換;解析学;力学系;摂動問題
      • Research on particular solutions and dynamics around them for Hamiltonian systems
        Grant-in-Aid for Young Scientists (B)
        Kyoto University;Osaka University
        Mitsuru Shibayama
        From 01 Apr. 2014, To 31 Mar. 2018, Project Closed
        力学系;非可積分性;変分法;微分ガロア理論;記号力学系;3体問題;Sitnikov問題;周期解;変分問題;可積分性;制限n体問題;n中心問題;ハミルトン力学系;天体力学
      • Understanding of turbulent phenomena through dissipative weak solutions to fluid equations
        Grant-in-Aid for Scientific Research (B)
        Kyoto University
        Takashi Sakajo
        From 01 Apr. 2014, To 31 Mar. 2018, Project Closed
        応用数学;流体力学;関数方程式論;数理物理;統計力学;乱流理論;渦力学;流体
      • Investigation of Diverse Bifurcation Structures in Differential Dynamical Systems
        Grant-in-Aid for Scientific Research (C)
        Kyoto University;Hiroshima University
        Kazuyuki Yagasaki
        From 01 Apr. 2013, To 31 Mar. 2016, Project Closed
        力学系;偏微分方程式系;不規則摂動系;周期摂動系;区分的に滑らかな系;分岐;カオス;非可積分性;微分方程式;反転可能系
      • Perturbation problems for degenerate integrable systems and mathematics for resonance phenomena
        Grant-in-Aid for Scientific Research (C)
        Kanazawa University
        HIdekazu Ito
        From 01 Apr. 2013, To 31 Mar. 2016, Project Closed
        可積分系;共鳴;超可積分系;シンプレクティック写像;標準形理論;標準形;ハミルトン系;可積分ベクトル場;超可積分性;バーコフ標準形
      • Variational approach to the n-body problem
        Grant-in-Aid for Young Scientists (B)
        Osaka University;Kyoto University
        Mitsuru SHIBAYAMA
        From 01 Apr. 2010, To 31 Mar. 2014, Project Closed
        多体問題;変分法;周期解;天体力学;力学系;カオス;分岐;対称性;特異点;スケーリング;ブローアップ;N体問題;ハミルトン力学系;衝突;摂動論;勾配法;峠の定理;特異点解析;可積分性
      • Normal forms for superintegrable systems at singular points and their perturbation problems
        Grant-in-Aid for Scientific Research (C)
        Kanazawa University
        Hidekazu ITO
        From 01 Apr. 2010, To 31 Mar. 2013, Project Closed
        超可積分系;ハミルトン系;バーコフ標準形;共鳴条件;標準形理論;ベクトル場;標準形;特異点;作用-角変数
      • Bifurcations and Homo- and Heteroclinic Behavior in Infinite- Dimensional Dynamical Systems
        Grant-in-Aid for Scientific Research (C)
        Hiroshima University;Niigata University
        Kazuyuki YAGASAKI
        From 01 Apr. 2009, To 31 Mar. 2013, Project Closed
        力学系;無限次元系;分岐;ホモ/ヘテロクリニック挙動;摂動法;微分ガロア理論;数値解析;パルス解;周期軌道;ホモ;ヘテロクリニック挙動

      External funds: others

      • Criterion of integrability based on blowing-up of singularities
        住友財団 基礎科学研究助成
        From 01 Nov. 2011, To 31 May 2013
        柴山允瑠
      list
        Last Updated :2022/05/14

        Education

        Teaching subject(s)

        • From Apr. 2015, To Mar. 2016
          Advanced Calculus II - Differential Equations
          Fall, 全学共通科目
        • From Apr. 2015, To Mar. 2016
          Mathematical Physics, Advanced
          Fall, 情報学研究科
        • From Apr. 2016, To Mar. 2017
          Applied Mathematics A1
          Fall, 工学部
        • From Apr. 2016, To Mar. 2017
          Advanced Calculus II - Differential Equations
          Fall, 全学共通科目
        • From Apr. 2016, To Mar. 2017
          Mathematical Physics, Advanced
          Fall, 情報学研究科
        • From Apr. 2017, To Mar. 2018
          ILAS Seminar
          Spring, 全学共通科目
        • From Apr. 2017, To Mar. 2018
          Applied Mathematics A1
          Fall, 工学部
        • From Apr. 2017, To Mar. 2018
          Advanced Calculus II - Differential Equations
          Fall, 全学共通科目
        • From Apr. 2017, To Mar. 2018
          Seminar on Applied Mathematics and Physics
          Fall, 工学部
        • From Apr. 2017, To Mar. 2018
          Mathematical Physics, Advanced
          Fall, 情報学研究科
        • From Apr. 2018, To Mar. 2019
          Mathematical Physics, Advanced
          Year-long, 情報学研究科
        • From Apr. 2019, To Mar. 2020
          Applied Mathematics A1
          Fall, 工学部
        • From Apr. 2019, To Mar. 2020
          Advanced Calculus II - Differential Equations
          Fall, 全学共通科目
        • From Apr. 2019, To Mar. 2020
          Mathematical Physics, Advanced
          Fall, 情報学研究科
        • From Apr. 2020, To Mar. 2021
          Applied Mathematics A1
          Fall, 工学部
        • From Apr. 2020, To Mar. 2021
          Advanced Calculus I - Vector Calculus
          Spring, 全学共通科目
        • From Apr. 2020, To Mar. 2021
          Mathematical Physics, Advanced
          Fall, 情報学研究科
        • From Apr. 2021, To Mar. 2022
          Applied Mathematics A1
          Fall, 工学部
        • From Apr. 2021, To Mar. 2022
          Applied Mathematics A2
          Spring, 工学部
        • From Apr. 2021, To Mar. 2022
          Advanced Calculus I - Vector Calculus
          Spring, 全学共通科目
        • From Apr. 2021, To Mar. 2022
          Mathematical Physics, Advanced
          Fall, 情報学研究科
        list
          Last Updated :2022/05/14

          Administration

          School management (title, position)

          • From 01 Apr. 2020, To 31 Mar. 2022
            京都大学教務事務電算管理運営委員会 委員

          Faculty management (title, position)

          • From 01 Apr. 2016, To 31 Mar. 2017
            情報セキュリティ委員会委員(情報セキュリティ副技術責任者)
          • From 01 Apr. 2016, To 31 Mar. 2017
            情報セキュリティ作業委員会委員
          • From 01 Apr. 2016, To 31 Mar. 2017
            計算機小委員会委員
          • From 01 Apr. 2017, To 31 Mar. 2018
            情報セキュリティ委員会委員
          • From 01 Apr. 2017, To 31 Mar. 2018
            情報セキュリティ作業委員会委員長
          • From 01 Apr. 2017, To 31 Mar. 2018
            計算機小委員会委員
          • From 01 Apr. 2019, To 31 Mar. 2021
            情報セキュリティ作業委員会委員
          • From 01 Apr. 2019, To 31 Mar. 2021
            計算機小委員会委員
          • From 01 Apr. 2021, To 31 Mar. 2022
            基盤整備委員会委員
          • From 01 Apr. 2021, To 31 Mar. 2022
            図書WG委員長

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