Toshiaki Fujiwara

Saari's homographic conjecture claims that, in the N-body problem under the
homogeneous potential, for , a motion having constant configurational measure is
homographic, wh...

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...

Donald Saari conjectured that the -body motion with constant
configurational measure is a motion with fixed shape. Here, the configurational
measure is a scale invariant product of the moment of inertia and the pote...

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...

Saari's homographic conjecture, which extends a classical statement proposed
by Donald Saari in 1970, claims that solutions of the Newtonian -body
problem with constant configurational measure are homographic. In other words,
if the mutual dist...

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...

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...

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...

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...

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...

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...