Table 1 System (24): Fixed-point map g with different choices of s
f(x) | s(x) | g(x) |
|---|---|---|
\(\begin{bmatrix} {x_{2}}x_{1}^{3}-1 \cr {x_{1}}x_{2}^{3}-1 \end{bmatrix} \) | \(\begin{bmatrix} {x_{1}} \cr {x_{2}} \end{bmatrix} \) | \(\begin{bmatrix} {x_{1}}-(2x_{1}^{3}x_{2}^{3} - 3x_{2}^{2} + x_{1}^{2})/(8x_{1}^{2}x_{2}^{3}) \cr {x_{2}}-(2x_{1}^{3}x_{2}^{3} - 3x_{1}^{2} + x_{2}^{2})/(8x_{1}^{3}x_{2}^{2}) \end{bmatrix} \) |
\(\begin{bmatrix} x_{1}^{3} \cr x_{2}^{3} \end{bmatrix} \) | \(\begin{bmatrix} \sqrt[3]{x_{1}^{3} - 3(2x_{1}^{3}x_{2}^{3} - 3x_{2}^{2} + x_{1}^{2})/(8x_{2}^{3}}) \cr \sqrt[3]{x_{2}^{3} - 3(2x_{1}^{3}x_{2}^{3} - 3x_{2}^{2} + x_{1}^{2})/(8x_{1}^{3}}) \end{bmatrix} \) |