Chapter 7.1, Problem 29E

In Exercises 24 through 29, consider a dynamical system
$\stackrel{\to }{x}(t+1)=A\stackrel{\to }{x}(t)$
with two components. The accompanying sketch shows the initial state vector ${\stackrel{\to }{x}}_0$ and two eigenvectors, ${\stackrel{\to }{\upsilon }}_1$ and ${\stackrel{\to }{\upsilon }}_2$ , of A (with eigenvalues ${\lambda }_1$ and ${\lambda }_2$ , respectively). For the given values of ${\lambda }_1$ and ${\lambda }_2$ , sketch a rough trajectory. Consider the future and the past of the system.

29. ${\lambda }_1=0.9,{\lambda }_2=0.9$