arXiv subjects

Atsushi Nagai

Publications and source records attributed to Atsushi Nagai.

4 recordsLinked to original sources

arXiv2021

On a parametrized difference equation connecting chaotic and integrable mappings

We present a new difference equation with two parameters c in [0,1] and A in [1,4]. This equation is equivalent to the logistic mapping if c=1 and the Morishita mapping if c=0, which are the well-known chaotic and integrable mappings, respectively. We first consider the case A=4 and investigate the time evolution by changing the parameter c in [0,1]. We next change both two parameters A in [3,4] and c in [0,1] and present the corresponding 3D bifurcation diagram.

nlin.CD↗

arXiv2014

The best constant of discrete Sobolev inequality on the C60 fullerene buckyball

The best constants of two kinds of discrete Sobolev inequalities on the C60 fullerene buckyball are obtained. All the eigenvalues of discrete Laplacian $A$ corresponding to the buckyball are found. They are roots of algebraic equation at most degree $4$ with integer coefficients. Green matrix $G(a)=(A+a I)^{-1}\ (0<a<\infty)$ and the pseudo Green matrix $G_*=A^{\dagger}$ are obtained by using computer software Mathematica. Diagonal values of $G_*$ and $G(a)$ are identical and they are equal to the best constants of discrete Sobolev inequalities.

math.FA↗

arXiv2002

Fractional Logistic Map

A new type of an integrable mapping is presented. This map is equipped with fractional difference and possesses an exact solution, which can be regarded as a discrete analogue of the Mittag-Leffler function.

nlin.SI↗

arXiv1995

Discrete soliton equations and convergence acceleration algorithms

Some of the well-known convergence acceleration algorithms, when viewed as two-variable difference equations, are equivalent to discrete soliton equations. It is shown that the $η-$algorithm is nothing but the discrete KdV equation. In addition, one generalized version of the $ρ-$algorithm is considered to be integrable discretization of the cylindrical KdV equation.

solv-int↗