Study the stability of the fixed point $(0,0)$ of the following planar linear difference system: $$x_{k+1}=\frac{3}{5}x_k+\frac{1}{5}y_k, \ y_{k+1}=\frac{1}{5}x_k+\frac{3}{5}y_k $$
Can somebody give me some ideas, please?
2026-04-07 14:40:47.1775572847
Stability of a fixed point of planar system
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Study the eigenvalues of the system $X_{n+1} = AX_n$, where $X_n = \begin{bmatrix} x_n \\ y_n \\ \end{bmatrix} $ and $A = \begin{bmatrix} \frac{3}{5} & \frac{1}{5} \\ \frac{1}{5} & \frac{3}{5} \\ \end{bmatrix} $