I would like to find the limit set $\omega(x)$ of the linear dynamical system

$$\mathrm f (x_1, x_2) = \begin{bmatrix} 2 & 1\\ 1 & 1\end{bmatrix} \begin{bmatrix} x_1\\ x_2\end{bmatrix}$$

I tried a few numerical values of $x_1$ and $x_2$ to see the sequence of vectors, but I'm not sure if this is right. I would appreciate your help.


closed as off-topic by Gabriel C. Drummond-Cole, Loïc Teyssier, Chris Godsil, ThiKu, RP_ May 11 '17 at 13:09

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  • $\begingroup$ The matrix is positive definite. What can you conclude from that? $\endgroup$ – Rodrigo de Azevedo May 11 '17 at 12:18
  • $\begingroup$ that all points are inside the omega limit set? $\endgroup$ – john May 11 '17 at 12:28
  • $\begingroup$ @john Search Anosov diffeomorphisms books.google.nl/… $\endgroup$ – Ali Taghavi May 11 '17 at 13:22
  • $\begingroup$ thank you, Ali Taghavi, though I learn from examples, and my lecturer gave me this example but I don't understand. $\endgroup$ – john May 11 '17 at 14:16