二、三次重根的无限时间能达丰富性计算

      当系统矩阵为二、三次重根的上约旦矩阵时，无限时间的能达丰富性分别为

      $\textrm{Vol}(R_{r,\infty})=\textrm{Vol}\left(C_{2}\left(\left[\Gamma,A\Gamma,A^{2}\Gamma,\cdots\right]\right)\right)$

                $=\textrm{Vol}\left(C_{2}\left(\left[\left[\begin{array}{c} 1\\ 0 \end{array}\right],\left[\begin{array}{c} \lambda\\ 1 \end{array}\right],\left[\begin{array}{c} \lambda^{2}\\ 2\lambda \end{array}\right],\cdots\right]\right)\right)$

                $=\sum_{(k_{1},k_{2})\in\Omega_{0,\infty}^{2}}\left|\mathrm{det}\left(\left[A^{k_{1}}\Gamma,A^{k_{2}}\Gamma\right]\right)\right|$

                $\textbfsymbol{=\frac{1}{\left(1-\lambda\right)^{2}\left(1-\lambda^{2}\right)}}$

与

      $\textrm{Vol}(R_{r,\infty})=\textrm{Vol}\left(C_{3}\left(\left[\Gamma,A\Gamma,A^{2}\Gamma,\cdots\right]\right)\right)$

              $=\textrm{Vol}\left(C_{2}\left(\left[\left[\begin{array}{c} 1\\ 0\\ 0 \end{array}\right],\left[\begin{array}{c} \lambda\\ 1\\ 0 \end{array}\right],\left[\begin{array}{c} \lambda^{2}\\ 2\lambda\\ 1 \end{array}\right],\left[\begin{array}{c} \lambda^{3}\\ 3\lambda^{2}\\ 3\lambda \end{array}\right],\left[\begin{array}{c} \lambda^{4}\\ 4\lambda^{3}\\ 6\lambda^{2} \end{array}\right],\cdots\right]\right)\right)$

              $=\sum_{(k_{1},k_{2},k_{3})\in\Omega_{0,\infty}^{3}}\left|\mathrm{det}\left(\left[A^{k_{1}}\Gamma,A^{k_{2}}\Gamma,A^{k_{3}}\Gamma\right]\right)\right|$

              $=\frac{1}{\left(1-\lambda\right)^{3}\left(1-\lambda^{2}\right)^{3}}$