Discrete systems of equations225(the Jordan form) and the transition matrix are:J=±1003²,V=±11−²Suppose for this system (u10,u20)=(5,2), then±u1tu2t²=±−²±1t0t−²−1±52²i.e.u1t=32+723tu2t=−32+723tTherefore, astincreasesu1t→+∞andu2t.Turning to the canonical form,z0=V−1u0, hence±z10z20²=±3/27/2²andz1t=1t³32´=32z2t=3t³72´Furthermore,z2tz1t=³31´t7/23/2=3t³73´and so for each point in the canonical phase space, the angle from the origin isincreasing, and so the direction of the system is vertically upwards, as illustratedin ±gure 5.5(b). Once again, the same instability is shown in the original space,±gure 5.5(a), and in its canonical form, ±gure 5.5(b). The fact that the trajectoryin ±gure 5.5(b) is vertical arises from the fact that rootr=1.Suppose one root is greater than unity in absolute value and the other less than
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