Question: phase plane of the system of difference equations

This question is related to the Question How do I plot phase plane

Thank you for suggestions. The system in matrix form looks like z(k+1)=Az(k). The solution to that is z(k)=A^kz(0). Now, phase planes of the system would look different for different matrix A (specifically, eigenvalues of A). For example, for complex eigenvalues phase plane would look like a spiral. I'm having difficulties plotting those phase planes. It's easy for differential equation, but I'm not sure how to work with system of difference equation in Maple.


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