Mitsuru Shibayama

Profile Information

Affiliation: Associate professor, Graduate School of Informatics, Kyoto University

J-GLOBAL ID: 201501015512056613
researchmap Member ID: 7000013549

External link: https://sites.google.com/view/mitsurushibayama/

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

Research Interests

Research Areas

Natural sciences / Mathematical analysis /

Research History

Jul, 2015

Associate Professor, Kyoto University
Apr, 2011

Associate Professor, Osaka University
Kyoto University

Papers

Braids, metallic ratios and periodic solutions of the 2n-body problem

Yuika Kajihara, Eiko Kin, Mitsuru Shibayama

Topology and its Applications, 337 108640-108640, Jul, 2023 Peer-reviewed
Variational proof of the existence of periodic orbits in the anisotropic Kepler problem

Shota Iguchi, Mitsuru Shibayama

Celestial Mechanics and Dynamical Astronomy, 135(3), May 4, 2023 Peer-reviewed
Variational proof of the existence of periodic orbits in the spatial Hill problem and its constrained problems

Shota Iguchi, Yuika Kajihara, Mitsuru Shibayama

Japan Journal of Industrial and Applied Mathematics, 40(1) 513-524, Sep 13, 2022 Peer-reviewed
Variational existence proof for multiple periodic orbits in the planar circular restricted three-body problem

Yuika Kajihara, Mitsuru Shibayama

Nonlinearity, 35(3) 1431-1446, Mar 3, 2022 Peer-reviewed
A mechanical true random number generator

Nozomi Akashi, Kohei Nakajima, Mitsuru Shibayama, Yasuo Kuniyoshi

New Journal of Physics, 24(1) 013019-013019, Jan 1, 2022 Peer-reviewed
Nonintegrability of the Reduced Planar Three-body Problem with Generalized Force

Mitsuru Shibayama, Junji Yamada

Regular and Chaotic Dynamics, 26(4) 439-455, 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-reviewedInvited
Variational proof of the existence of brake orbits in the planar 2-center problem

Yuika Kajihara, Mitsuru Shibayama

Discrete and Continuous Dynamical Systems-A, 39(10) 5785-5797, Oct, 2019 Peer-reviewed
Variational Construction of Orbits Realizing Symbolic Sequences in the Planar Sitnikov Problem

Mitsuru Shibayama

Regular and Chaotic Dynamics, 24(2) 202-211, 2019 Peer-reviewed
Non-integrability of the spacial n-center problem

Mitsuru Shibayama

Journal of Differential Equations, 265(6) 2461-2469, Sep 15, 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, 51(31), Aug, 2018 Peer-reviewed
PERIODIC SOLUTIONS FOR A PRESCRIBED-ENERGY PROBLEM OF SINGULAR HAMILTONIAN SYSTEMS

Mitsuru Shibayama

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 37(5) 2705-2715, May, 2017 Peer-reviewed
Three topologically nontrivial choreographic motions of three bodies

Milovan Suvakov, Mitsuru Shibayama

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 124(2) 155-162, Feb, 2016 Peer-reviewed
NON-INTEGRABILITY CRITERION FOR HOMOGENEOUS HAMILTONIAN SYSTEMS VIA BLOWING-UP TECHNIQUE OF SINGULARITIES

Mitsuru Shibayama

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 35(8) 3707-3719, Aug, 2015 Peer-reviewed
Minimax approach to the n-body problem

Mitsuru Shibayama

NONLINEAR DYNAMICS IN PARTIAL DIFFERENTIAL EQUATIONS, 64 221-228, 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, 214(1) 77-98, 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, 110(1) 53-70, May, 2011 Peer-reviewed
NON-INTEGRABILITY OF THE COLLINEAR THREE-BODY PROBLEM

Mitsuru Shibayama

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 30(1) 299-312, May, 2011 Peer-reviewed
Minimizing Periodic Orbits with Regularizable Collisions in the n-Body Problem

Mitsuru Shibayama

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 199(3) 821-841, Mar, 2011 Peer-reviewed
Heteroclinic connections between triple collisions and relative periodic orbits in the isosceles three-body problem

Mitsuru Shibayama, Kazuyuki Yagasaki

NONLINEARITY, 22(10) 2377-2403, Oct, 2009 Peer-reviewed

Misc.

微分形式と力学

柴山允瑠

数理科学, 61(8) 16-23, Aug, 2023 InvitedLead author
古典力学と変分問題 : n体問題の周期解の存在証明に向けて(第12回)8の字解の存在証明以降の展開

柴山允瑠

数学セミナー, 62(3), Mar, 2023
古典力学と変分問題 : n体問題の周期解の存在証明に向けて(第11回)最小点の存在証明

柴山允瑠

数学セミナー, 62(2), Feb, 2023
古典力学と変分問題 : n体問題の周期解の存在証明に向けて(第10回)最小点の存在に関する反例

柴山允瑠

数学セミナー, 62(1), Jan, 2023
古典力学と変分問題 : n体問題の周期解の存在証明に向けて(第9回)8 の字解の存在証明 (2)

柴山允瑠

数学セミナー, 61(12) 75-79, Dec, 2022
古典力学と変分問題 : n体問題の周期解の存在証明に向けて(第8回)8 の字解の存在証明 (1)

柴山允瑠

数学セミナー, 61(11) 74-77, Nov, 2022
古典力学と変分問題 : n体問題の周期解の存在証明に向けて(第7回)n体問題の変分構造と対称性

柴山允瑠

数学セミナー, 61(10) 81-85, Oct, 2022
古典力学と変分問題 : n体問題の周期解の存在証明に向けて(第6回)n 体問題の中心配置と自己相似解

柴山允瑠

数学セミナー, 61(9) 88-93, Sep, 2022
古典力学と変分問題 : n体問題の周期解の存在証明に向けて(第5回)特異点をもつポテンシャル系の周期解

柴山允瑠

数学セミナー, 61(8) 88-92, Aug, 2022
古典力学と変分問題 : n体問題の周期解の存在証明に向けて(第4回)中心力の周期解

柴山允瑠

数学セミナー, 61(7) 76-81, Jul, 2022
古典力学と変分問題 : n体問題の周期解の存在証明に向けて(第3回)周期解の存在

柴山允瑠

数学セミナー, 61(6) 89-93, Jun, 2022
『スウガクセミナー』ソウカン 60シュウネンキネンゴウ

61(5) 85-89, May, 2022
古典力学と変分問題 : n体問題の周期解の存在証明に向けて(第1回)古典力学の変分構造

柴山允瑠

数学セミナー, 61(4) 86-90, Apr, 2022
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, 2181 183-195, 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, 2181 71-83, 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, 2181 112-125, 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, 54(4) 37-43, 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, 1993 71-78, 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, 1827 1-17, 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), 56th ROMBUNNO.313, 2013

Books and Other Publications

ハミルトン力学系

柴山允瑠

サイエンス社, Dec, 2016

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

Professional Memberships

The Mathematical Society of Japan

Research Projects

変分法と位相幾何学によるハミルトン系の新たな理論の構築と展開

科学研究費助成事業, 基盤研究(B), 日本学術振興会, Apr, 2023 - Mar, 2028

柴山允瑠, 金英子, 梶原唯加
Development of innovative theories on integrability of dynamical systems and their applications

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B), Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, Apr, 2022 - Mar, 2026
変分的および幾何学的手法による人工衛星と惑星探査機の軌道設計

さきがけ, 科学技術振興機構, Oct, 2021 - Mar, 2025
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

科学研究費助成事業基盤研究(C), 基盤研究(C), 日本学術振興会, Apr, 2018 - Mar, 2023

柴山允瑠
標準形理論による可積分系の剛性と大域構造の解析

科学研究費助成事業基盤研究(C), 基盤研究(C), 日本学術振興会, Apr, 2016 - Mar, 2022

伊藤秀一, 柴山允瑠
Research on particular solutions and dynamics around them for Hamiltonian systems

Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B), Grant-in-Aid for Young Scientists (B), Japan Society for the Promotion of Science, Apr, 2014 - Mar, 2019

Shibayama Mitsuru
Understanding of turbulent phenomena through dissipative weak solutions to fluid equations

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B), Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, Apr, 2014 - Mar, 2018

Sakajo Takashi, FUJIWARA Hiroshi, GOTODA Takeshi
Perturbation problems for degenerate integrable systems and mathematics for resonance phenomena

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2013 - Mar, 2017

Ito HIdekazu, YAGASAKI Kazuyuki
Investigation of Diverse Bifurcation Structures in Differential Dynamical Systems

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2013 - Mar, 2017

Yagasaki Kazuyuki
Variational approach to the n-body problem

Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B), Grant-in-Aid for Young Scientists (B), Japan Society for the Promotion of Science, Apr, 2010 - Mar, 2014

SHIBAYAMA Mitsuru
Normal forms for superintegrable systems at singular points and their perturbation problems

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2010 - Mar, 2013

ITO Hidekazu, YAGASAKI Kazuyuki, SHIBAYAMA Mitsuru
Bifurcations and Homo- and Heteroclinic Behavior in Infinite- Dimensional Dynamical Systems

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2009 - 2012

YAGASAKI Kazuyuki, ITO Hidekazu, SHIBAYAMA Mitsuru

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

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