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Math 2890 Sample Exam Problems

Analyze a discrete dynamical system

Let $A=\left(\begin{array}{rrrr} 254.1 & 45.6 & -36.8 & -29.2 \\ -785.2 & -139.9 & 114.2 & 91 \\ -81 & -12.6 & 12.8 & 10.8 \\ 1073.1 & 191.7 & -156 & -124 \end{array}\right)$.

Is the origin an attractor, repeller or saddle point for the discrete dynamical system $x_{k+1} = A x_k$? How do you know?

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