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• # Artykuł - szczegóły

## Annales Polonici Mathematici

2011 | 102 | 2 | 143-159

## Analytic solutions of a nonlinear two variables difference system whose eigenvalues are both 1

EN

### Abstrakty

EN
For nonlinear difference equations, it is difficult to obtain analytic solutions, especially when all the eigenvalues of the equation are of absolute value 1. We consider a second order nonlinear difference equation which can be transformed into the following simultaneous system of nonlinear difference equations:
⎧ x(t+1) = X(x(t),y(t))

⎩ y(t+1) = Y(x(t), y(t))
where $X(x,y) = λ₁x + μy + ∑_{i+j≥2} c_{ij}x^{i}y^{j}$, $Y(x,y) = λ₂y + ∑_{i+j≥2} d_{ij}x^{i}y^{j}$ satisfy some conditions. For these equations, we have obtained analytic solutions in the cases "|λ₁| ≠ 1 or |λ₂| ≠ 1" or "μ = 0" in earlier studies. In the present paper, we will prove the existence of an analytic solution for the case λ₁ = λ₂ = 1 and μ = 1.

143-159

wydano
2011

### Twórcy

autor
• Department of Mathematics, College of Liberal Arts, J. F. Oberlin University, 3758 Tokiwa-cho, Machida-City, Tokyo, 194-0294, Japan