Toshiaki Fujiwara on ResearchGate

Toshiaki Fujiwara on researchmap

N-body

• Equivalence of Rigid Motions and Relative Equilibria in the N-Body Problem on the Two-Sphere
  with Ernesto Pérez-Chavela, and Shuqiang Zhu
  • Preprint: https://arxiv.org/abs/2409.16545
  
  
• Mass independent shapes for relative equilibria in the two dimensional positive curved three body problem
  with Ernesto Perez-Chavela
  • Preprint: https://arxiv.org/abs/2311.02770
  • Published: https://doi.org/10.1007/s00332-024-10065-z
  
  
• Continuations and bifurcations of relative equilibria for the positive curved three body problem
  with Ernesto Perez-Chavela
  • Preprint: https://arxiv.org/abs/2306.13838
  • List of the 73 Lagrange shapes: 73LagrangeShapes20231108.pdf
  • Published: https://doi.org/10.1134/S1560354724560028
  
  
• Three body relative equilibria on S^2
  with Ernesto Perez-Chavela
  • Preprint: https://arxiv.org/abs/2309.06603
  • Published: https://doi.org/10.1134/S1560354723040111

• Equal masses Eulerian relative equilibria on a rotating meridian of S^2
  with Ernesto Perez-Chavela
  • Preprint: https://arxiv.org/abs/2203.14930
  
  
• Three-body relative equilibria on S^2
  II: Extended Lagrangian configurations
  with Ernesto Perez-Chavela
  • Preprint: https://arxiv.org/abs/2202.12708
  
  
• Three-body relative equilibria on S^2
  I: Euler configurations
  with Ernesto Perez-Chavela
  • Preprint: https://arxiv.org/abs/2202.10351

• Variational Principle of Action and Group Theory for Bifurcation of Figure-eight solutions
  with Hiroshi Fukuda and Hiroshi Ozaki
  • Preprint: https://arxiv.org/abs/1905.11073
  • Talk at Celestial Mechanics and Beyond http://celmech.itam.mx:8080 March 9--13, 2020, Puebla, Mexico.
    Slides: bifurcationsAndSymmetry19finalWcomments.pdf (7.3MB)

• Variational principle for bifurcation in Lagrangian mechanics
  with Hiroshi Fukuda and Hiroshi Ozaki
  • Preprint: https://arxiv.org/abs/1905.11073
  
  
• Morse index and bifurcation for figure-eight choreographies of the equal mass three-body problem
  with Hiroshi Fukuda and Hiroshi Ozaki
  • Published: J. Phys. A: Math. Theor. 52 185201 (2019)
    
  • DOI: https://doi.org/10.1088/1751-8121/ab1270
  • Preprint: https://arxiv.org/abs/1901.00115v2

• 三体8の字解の分岐--作用と線形安定性の視点から--
  Bifurcations of figure-eight --Morse index and characteristic multipliers--
  with 福田宏， 尾崎浩司
  • 冬の力学系研究集会（軽井沢）での講演
  • Slides: 20190912Karuizawa6.pdf(16.9MB)
  • Characteristic multipliers of the figure-eight in -1 < \alpha < 2.5
  • Bifurcated solutions at \alpha=-0.21...
  
  
• 三体8の字解とそれから分岐する解の線形安定性 --5周期分岐--
  with 福田宏， 尾崎浩司
  • 応用数理学会2018年度年会 名古屋大学での講演
  • スライド: 20180903jsiamNagoya04s.pdf
  
  
• Linear stability and Morse index for the figure-eight and k=5 slalom solutions under homogeneous potential
  with Hiroshi Fukuda and Hiroshi Ozaki
  • Talk at AIMS 2018 Taipei, Taiwan
  • slides: 2018AIMSTaipei09final.pdf
  • Movie: Eigenvalues for Floquet matrix for the figure-eight solution

• Eigenvalues and eigenfunctions for second derivative of the action at the figure-eight and slalom solutions
  with Hiroshi Fukuda and Hiroshi Ozaki
  • Talk at Institute of Classical Mechanics 2018 at Mitaka （天体力学N体力学研究会 2018 三鷹）
  • slides: 2018NAOMitaka09final.key.pdf
  • appendix: Decomposition of the Hessian matrix for action at choreographic three-body solutions with figure-eight symmetry
  
  
• Morse index for figure-eight choreographies of the planar equal mass three-body problem
  with Hiroshi Fukuda and Hiroshi Ozaki
  • Published: Journal of Physics A: Mathematical and Theoretical, Volume 51, 145201
    
  • DOI: https://doi.org/10.1088/1751-8121/aab06d
  • Preprint: https://arxiv.org/abs/1710.04834
  
  
• Figure-eight and Slalom solutions in function space
  • Talk at MCA 2017, Montreal, Canada
  • slides: 2017Montreal0728final.pdf
  • Movies for slalom solutions S1, S2 and S3
  
  
• Decomposition of matrix for second derivative of action at choreographic three-body solutions
  • Talk at 2017　RIMS Workshop, Dynamical Systems — Joint Exploration of Theory and Application
    （平成29年度　RIMS共同研究, 力学系 — 理論と応用の連携探索）
  • slides: 20170607KyotoVer0607p4.pdf

• Numerical investigations of Slalom solutions
  • Talk at 天体力学N体力学2017（東工大）(2017/03/22)
  • PDF: slalom10.pdf
  
  
• Figure-eight solution in the complex time plane
  
  • Talk: 25回ハミルトン系力学セミナー＠金沢大学, December 2, 2016
  • PDF: 20161211KanazawaEp.pdf
  
  
• Geometric, algebraic, and analytic properties of figure-eight solution (2016/08/03)
  Talk at Sub-Riemannian Geometry and Celestial Mechanics: A conference to celebrate the 60th birthday of Richard Montgomery.
  
  • Slides in HTML: http://www.clas.kitasato-u.ac.jp/~fujiwara/nBody/20160803TalkFujiwaraWithComment/
  • Site for this conference: http://montgomery.eventos.cimat.mx
  
  
• Figure-eight choreographies of the equal mass three-body problem with Lennard-Jones-type potentials
  with Hiroshi Fukuda and Hiroshi Ozaki
  • Published: Journal of Physics A: Mathematical and Theoretical, Volume 50, Number 10
  • DOI: 10.1088/1751-8121/aa5741
  • Preprint: http://arxiv.org/abs/1606.08760
  • Definition and animations and by Hiroshi Fukuda http://kilin.clas.kitasato-u.ac.jp/3body/
  • Animations by myself
  • Lennard-Jonesポテンシャルのもとでの三体8の字解（日本語）

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• 北里大学一般教育部セミナー(2016/01/18)
  • スライド( 9枚/page ) 15MB 20160118KitasatoTalk.Small.pdf
  • スライド( 1枚/page ) 15MB 20160118KitasatoTalk.Large.pdf
  
  
• 天体力学N体力学2015（千葉）(2015/12/24)
  • スライド 14MB fig8ComplexPlane7.20151226withComments.pdf
  
  
• Three-body Choreographies by Suvakov and Shibayama
  Three-body Choreographies by Suvakov and Shibayama
  
  

  ---

• Saari's homographic conjecture for general masses in planar three-body problem under Newton potential and a strong force potential
  with Hiroshi Fukuda, Hiroshi Ozaki and Tetsuya Taniguchi
  This work was supported by JSPS KAKENHI Grant Number 23540249.
  • Published:J. Phys. A: Math. Theor. 48 (2015) 265205.
    doi:10.1088/1751-8113/48/26/265205
  • Preprint: http://arxiv.org/abs/1503.00407
  
  
• Saari's homographic conjecture for planar equal-mass three-body problem in Newton gravity
  with Hiroshi Fukuda, Hiroshi Ozaki and Tetsuya Taniguchi
  This work was supported by JSPS KAKENHI Grant Number 23540249.
  • Published: J. Phys. A: Math. Theor. 45 (2012) 345202.
    doi:10.1088/1751-8113/45/34/345202
  • Preprint: http://arxiv.org/abs/1202.0893
  • Talk at "2011 年度冬の力学系研究集会", Karuizawa, Nagano, Japan on Jan. 7 2011.
    http://www.math.titech.ac.jp/~nsumi/symposium/dyn11program.pdf
    • Slides: 20120107Karuizawa5final2.pdf
  
  
• Saari's homographic conjecture for planar equal-mass three-body problem under a strong force potential
  with Hiroshi Fukuda, Hiroshi Ozaki and Tetsuya Taniguchi
  This work was supported by JSPS KAKENHI Grant Number 23540249.
  • Published: 2012 J. Phys. A: Math. Theor. 45 045208
    doi: 10.1088/1751-8113/45/4/045208
  • Preprint:
    from JAPAN: http://jp.arxiv.org/abs/1107.2178
    from other: http://arxiv.org/abs/1107.2178
  • Talk at "THE SYMPOSIUM ON CELESTIAL MECHANICS 天体力学Ｎ体力学研究会 2011" Osaka, Sept. 1--2, 2011. http://www.sigmath.es.osaka-u.ac.jp/~shibayama/nbody11/index.html
    • slides (HTML) movies need QuickTime
    • slides (PDF: 20110902.9finalp4s.pdf)
    • 20110902.9finalp.key (for Macintosh KeyNote)
  • Resultant（終結式）について： resultant3.pdf
  
  
• Three-Body Choreographies in Given Curves
  with Hiroshi Ozaki, Hiroshi Fukuda
  • Published: J. Phys. A: Math. Theor. 42 395205
    doi: 10.1088/1751-8113/42/39/395205
  • Preprint:
    from JAPAN: http://xxx.yukawa.kyoto-u.ac.jp/abs/0906.2249
    from other: http://arxiv.org/abs/0906.2249
  • Three Points Theorem (Theorem and animations)
  • 三点定理（定理とアニメーション）
  
  
  • Animations for Three Points Theorem by Hiroshi Fukuda
  
  
• Saari's Homographic Conjecture of the Thtree-Body Problem
  with Florlin Diacu, Ernesto Perez-Chavela, Manuele Santoprete
  • Published: Transactions of the American Mathematical Society, 360-12, pp. 6447--6473, 2008
  
  
• No quartic curve supports 3-body figure-eight solution under homogeneous potential
  with Hiroshi Fukuda and Hiroshi Ozaki
  • Talk at Hamsys 2008, Guanajuato, Mexico
    Slides:fujiwaraHamsys2008v10.pdf
  • Abstracts: abstracts.pdf
  • Poster: hamsys2008.pdf
  • Schedule: Schedule.pdf
  
  
• Synchronised Similar Triangles for Three-Body Orbit with Zero Angular Momentum
  with Hiroshi Fukuda, Atsushi Kameyama, Hiroshi Ozaki and Michio Yamada
  • Published: J. Phys. A: Math. Gen. 37 (2004) 10571-10584.
    
  • Preprint:
    from JAPAN: http://xxx.yukawa.kyoto-u.ac.jp/abs/math-ph/0404056
    from other: http://arxiv.org/abs/math-ph/0404056
    
  • Talk at SPT2004, Cala Gonone, Sardinia, Italy
    Slides:
    • KeyNote: SPT2004.ver09.key.tar(7.2MB)
    • PowerPoint for Macintosh: SPT2004.ver09.ppt.tar(8MB)
    • PowerPoint for Windows: spt2004ppt.lzh(5MB)
    • PDF: SPT2004.ver09.pdf(1.1MB)
    QuickTime Animations:
    • The figure-eight: mov.X.mov
    • Three tangents: mov.3Tangents.mov
    • Three tangents, three normals and circumcircle: mov.fig8AlphaEqMinus2.CtCnCoCf.mov
    • Synchronised Similar Triangles mov.xvTriangle.small.mov
    AVI Animations:
    • The figure-eight: mov.X.avi
    • Three tangents: mov.3Tangents.avi
    • Three tangents, three normals and circumcircle: mov.fig8AlphaEqMinus2.CtCnCoCf.avi
    • Synchronised Similar Triangles mov.xvTriangle.small.avi
    SPT2004 home page
  
  
• Orbits with zero angular momentum and constant moment of inertia have remarkable geometrical properties
  with Hiroshi Fukuda, Atsushi Kameyama, Hiroshi Ozaki and Michio Yamada
  • Talk at Hakone N-body on March 2, 2004:
    "Synchronized Triangles in the Figure-Eight Solution under 1/r^2 Potential"
    Slides are available in two formats:
    • KeyNote: hakone2004.ver8.key.tgz (gziped tar file of KeyNote: 2.8MB)
      You need "KeyNote" application (by Apple. Not Free) to read this beautyful document.
    • PDF: hakone2004.ver7.3.pdf(PDF: 2.6MB)
      
    Movies/Animation
    • GIF animations:
      • Centers ( The "center of tangents", "center of normals", the circumcenter and the "center of force". )
      • Synchronized Triangles
      • Shape of the figure-eight orbit for $\alpha$.
      
      
    • The same animations by QuickTime movie: (Get QuickTime player for Windows/Macintosh)
      • Centers ( The "center of tangents", "center of normals", the circumcenter and the "center of force". )
      • Synchronized Triangles
      • Shape of the figure-eight orbit for $\alpha$.
      
      
    Program( in Japanese )
    
  
  
• Talk at RIMS(Research Institute for Mathematical Sciences) on Nov. 13, 2003.
  Talk at Department of Mathematics, Kyoto University on Nov. 14, 2003.
  Slides are available in three formats:
  • KeyNote: rims2003.full.key.tar.gz(3.4MB)
    This is the original format. Lots of figs and movies are included. You need "KeyNote" application (by Apple. Not Free) to read this beautyful document.
  • PDF : rims2003.full.pdf.tar.gz(3.1MB)
    Exported from the original format. (Sorry, movies don't move.)
  • PPT : rims2003.full.ppt.tar.gz(6.9MB)
    Exported from the original format. Lots of figs and movies are included. You need "PowerPoint" application (by microsoft. Not Free) or compatible to read this document. Sorry, this is not beautiful and file size is so big.
  Abstract:RIMS2003Abstract.pdf (PDF in Japanese. 196KB)
  Proceedings
  
  • Proceedungs for "Developments and Applications of Dynamical Systems Theory" at RIMS 2003
    
  • Our paper: "N-body Choreography on the Lemniscate (Developments and Applications of Dynamical Systems Theory)"
    
  RIMS (Research Institute for Mathematical Sciences)
  
• Convexity in the Figure Eight Solution to the Three-Body Problem
  • Published:Pacific Journal of Mathematics Vol. 219, No.2 (April 2005) 271--283
  • with Richard Montgomery
  • TeX source
  • Preprint:
    from JAPAN: http://xxx.yukawa.kyoto-u.ac.jp/abs/math.DS/0308252
    from other: http://arxiv.org/abs/math.DS/0308252
    also appear in AIM preprint Series 2003-15: http://front.math.ucdavis.edu/math.DS/0308252
  • Acknowledgment: The authors would like to thank AIM/ARCC for funding a workshop in celestial mechanics where the authors met.
    AIM/ARCC HomePage
    workshop "Variational methods in Celestial mechanics"
    door to AIM: AIM.gif(266 KB)
  
  
• Evolution of the Moment of Inertia of Three-Body Figure-Eight Choreography
  (Non-Conservation of the Moment of Inertia of Three-Body Figure-Eight Choreography)
  • Published: J. Phys. A: Math. Gen. 36 (24 October 2003) 10537-10549
  • with Hiroshi Fukuda and Hiroshi Ozaki
  • Preprint:
    from JAPAN: http://xxx.yukawa.kyoto-u.ac.jp/abs/math-ph/0304014
    from other: http://arXiv.org/abs/math-ph/0304014
  • Talk at EquaDiff 2003. (PDF file:fujiwaraEquaDiffTalk.pdf(113KB))
    EquaDiff 2003 HomePage
  
  
• Choreographic Three Bodies on the Lemniscate
  
  • Published: J. Phys. A: Math. Gen. 36 (21 March 2003) 2791-2800
  • with Hiroshi Fukuda and Hiroshi Ozaki
  • Preprint:
    from JAPAN: http://xxx.yukawa.kyoto-u.ac.jp/abs/math-ph/0210044
    from other: http://arXiv.org/abs/math-ph/0210044
    
  • GIF animation:
    • Center of Mass at t=T/4 is at the origin if and only if k^2=(2+sqrt{3})/4
    • x(t),v(t),a(t) (Corrected 1/29/2004)
    • Potential Surface
    • Three tangent lines from the three bodies meet at a point on the rectangular hyperbola (updated 11/05/2002)
  
  
• Review of Several Motions on the Lemniscate. (2/6/2003) motionOnLemniscate.pdf (PDF 147KB)
• Lecture at University of Shizuoka on Feb. 5, 2003. (PDF in Japanese lecture2.5.2003.pdf(615KB))