Linear discrete dynamical system

Let :           u_n+1 = a11 u_n + a12 v_n    
                v_n+1 = a21 u_n + a22 v_n 

                   
If you write :   (t : transpose)        

         X_n  = [u_n, v_n]t             
   and                            then    X_n+1 = A X_n
        X_n+1 = [u_n+1,v_n+1]t


      Let's put     X_0 = [u_0,v_0]t
          
          then      X_1 = A X_0
                    X_2 = A X_1 = A^2 X_0
                    X_3 = A X_2 = A^3 X_0  
                           ...
                    X_n =  A^n X_0                              
       

       Calculate : lim X_n = 
                   n-> oo

For this, we will use eigenvalues ​​and eigenvectors for the first method, and for the second method we will directly calculate the power of A.
        
        

Exemple 1 :

• c00a.c  : Let's calculate the eigenvectors and eigenvalues
• c00b.c  : Calculate A^P

We will be able to observe that from P = 19, the value of A^P no longer changes.

Exemple 2 :

• c00c.c  : Let's calculate the eigenvectors and eigenvalues
• c00d.c Calculate A^P

We will be able to observe that from P = 17, the value of A^P no longer changes.