Toshiaki Fujiwara

J-GLOBAL         Last updated: Apr 21, 2019 at 22:22
 
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Name
Toshiaki Fujiwara
Nickname
fujiwaraToshiaki
URL
http://www.clas.kitasato-u.ac.jp/~fujiwara/
Affiliation
Kitasato University
Job title
Professor emeritus
Degree
Ph.D(Kyoto University)
Research funding number
00173493
Twitter ID
fujiwaraToshiak
ORCID ID
0000-0002-6396-3037

Published Papers

 
Morse index and bifurcation for figure-eight choreographies of the equal mass three-body problem
Hiroshi Fukuda, Toshiaki Fujiwara, Hiroshi Ozaki
Journal of Physics A: Mathematical and Theoretical   52(18)    Apr 2019   [Refereed]
Hiroshi Fukuda, Toshiaki Fujiwara, Hiroshi Ozaki
Journal of Physics A: Mathematical and Theoretical,   51(14)    Mar 2018   [Refereed]
Hiroshi Fukuda, Toshiaki Fujiwara, Hiroshi Ozaki
Journal of Physics A: Mathematical and Theoretical   50(10)    Feb 2017   [Refereed]
Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki, Tetsuya Taniguchi
J. Phys. A   48    Jun 2015   [Refereed]
Saari's homographic conjecture claims that, in the N-body problem under the
homogeneous potential, Tex for Tex, a motion having constant configurational measure Tex is
homographic, wh...
Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki, Tetsuya Taniguchi
J. Phys. A:Math. Theor.   45    Aug 2012   [Refereed]
Saari's homographic conjecture in N-body problem under the Newton gravity is
the following; configurational measure \mu=\sqrt{I}U, which is the product of
square root of the moment of inertia I=(\sum m_k)^{-1}\sum m_i m_j r_{ij}^2 and
the potentia...
Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki, Tetsuya Taniguchi
2012 J. Phys. A: Math. Theor. 45 045208      Jan 2012   [Refereed]
Donald Saari conjectured that the Tex-body motion with constant
configurational measure is a motion with fixed shape. Here, the configurational
measure Tex is a scale invariant product of the moment of inertia Tex and the pote...
Hiroshi Ozaki, Hiroshi Fukuda, Toshiaki Fujiwara
2009 J. Phys. A: Math. Theor. 42 395205   42(39)    Sep 2009   [Refereed]
As shown by Johannes Kepler in 1609, in the two-body problem, the shape of
the orbit, a given ellipse, and a given non-vanishing constant angular momentum
determines the motion of the planet completely.
Even in the three-body problem, in some ca...
Florin Diacu, Toshiaki Fujiwara, Ernesto Perez-Chavela, Manuele Santoprete
Trans. Amer. Math. Soc. 360 (2008), 6447-6473   360 6447-6473   May 2008   [Refereed]
Saari's homographic conjecture, which extends a classical statement proposed
by Donald Saari in 1970, claims that solutions of the Newtonian Tex-body
problem with constant configurational measure are homographic. In other words,
if the mutual dist...
Toshiaki Fujiwara, Richard Montgomery
Pacific Journal of Mathematics   219(2) 271-283   2005   [Refereed]
The figure eight is a remarkable solution to the Newtonian three-body problem in which the three equal masses chase each around a planar curve having the qualitative shape and symmetries of a figure eight. Here we prove that each lobe of this eigh...
Toshiaki Fujiwara, Hiroshi Fukuda, Atsushi Kameyama, Hiroshi Ozaki and Michio Yamada
Journal of Physics A: Mathemathical and General   37(44) 10571-10584   Oct 2004   [Refereed]
If the moment of inertia is also constant along the orbit, the triangle whose vertexes are the positions of the bodies, and the triangle whose perimeters are the momenta of the bodies, are always similar ('synchronized similar triangles'). This si...
Hiroaki Arisue, Toshiaki Fujiwara, K. Tabata
Nuclear Physics B - Proceedings Supplements   129--130 774-776   Mar 2004
The new algorithm of the finite lattice method is applied to generate the high-temperature expansion series of the simple cubic Ising model to β^{50} for the free energy, to β^{32} for the magnetic susceptibility and to β^{29} for the second momen...
Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki
Journal of Physics A: Mathematical and General, volume 36, issue 42, pages 10537 - 10549, (2003)   36    Oct 2003   [Refereed]
We investigate three-body motion in three dimensions under the interaction
potential proportional to r^alpha (alpha \neq 0) or log r, where r represents
the mutual distance between bodies, with the following conditions: (I) the
moment of inertia i...
Hiroaki Arisue, Toshiaki Fujiwara
Physical Review E   67    Jun 2003   [Refereed]
We propose a new algorithm of the finite lattice method to generate the
high-temperature series for the Ising model in three dimensions. It enables us
to extend the series for the free energy of the simple cubic lattice from the
previous series of...
Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki
J. Phys. A36, 2791--2800 (2003)   36(11) 2791-2800   Mar 2003   [Refereed]
We show that choreographic three bodies {x(t), x(t+T/3), x(t-T/3)} of period
T on the lemniscate, x(t) = (x-hat+y-hat cn(t))sn(t)/(1+cn^2(t)) parameterized
by the Jacobi's elliptic functions sn and cn with modulus k^2 = (2+sqrt{3})/4,
conserve the...
HiroakiArisue, ToshiakiFujiwara, Yumi S.Hirata
Journal of Computational Physics   111(1) 156-164   1994   [Refereed]
Hiroaki Arisue, Toshiaki Fujiwara
Nuclear Physics B   285 253-263   1987   [Refereed]
Hiroaki Arisue, Toshiaki Fujiwara, Mitsuhiro Kato, and Kaku Ogawa
Physical Review D   35(8)    1987   [Refereed]
Hiroaki Arisue, Toshiaki Fujiwara
Progress of Theoretical Physics   72(6) 1176-1196   1984   [Refereed]
Hiroaki Arisue, Toshiaki Fujiwara
Progress of Theoretical Physics   71(5) 1026-1035   1984   [Refereed]
Hiroaki Arisue, Toshiaki Fujiwara
Progress of Theoretical Physics   70(1) 229-248   1983   [Refereed]

Misc

 
Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki
arXiv      Nov 2018
We developed a method to calculate the eigenvalues and eigenfunctions of the second derivative (Hessian) of action at choreographic three-body solutions that have the same symmetries as the figure-eight solution. A choreographic three-body solutio...
Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki
RIMS Kokyuroku   1369 163-177   2004
We show that the lemniscate curve is the simplest candidate of the orbit for the Tex body figure eight choreography. Here figure eight choreography is the periodic motion of equal masses with equal time spacing o...

Conference Activities & Talks

 
Linear stability and Morse index for the figure-eight and k=5 slalom solutions under homogeneous potential
Toshiaki ujiwara
AIMS 2018   5 Jul 2018   
Eigenvalues and eigenfunctions for second derivative of the action at the figure-eight and slalom solutions
Toshiaki Fujiwara
Institute of Classical Mechanics 2018   10 Mar 2018   
Figure-eight and Slalom solutions in function space
Toshiaki Fujiwara
Mathematical Congress of Americs   28 Jul 2017   
Decomposition of matrix for second derivative of action at choreographic three-body solutions
Toshiaki Fujiwaa
Dynamical Systems -- Joint Exploration of Theory and Application   7 Jun 2017   
Numerical investigations of Slalom solutions
Toshiaki Toshiaki
Institute of Classical Mechanics 2018   22 Mar 2017   

Research Grants & Projects

 
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research
Project Year: 2011 - 2013    Investigator(s): Toshiaki Fujiwara
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(C))
Project Year: 2007 - 2008    Investigator(s): Toshiaki Fujiwara