5) [4 points] A nonlinear system and one point ($p_1, q_1$) of an m-cycle is given.
$\begin{cases} x_{n+1} = 3 - x_n^2 \ y_{n+1} = 2y_n \end{cases}$, ($p_1, q_1$) = (2, 0)
a) Find the fixed points and determine their local stability (Sink, source, saddle?)
b) Find the other points of the m-cycle and the period of the cycle and determine the
local stability or instability of the cycle with reasoning(you can do your computations
for the values on the computer).
