#OK to post homework

#Nicholas DiMarzio, 10/04/21, Assignment 8

#

Problem 1

#

a1=1, a2=8, a3=1, a4=1

F(x)=(1+8x)/(1+x)





f := (1 + 8*(x - 1))/(1 + (x - 1))

#*find first 1000 terms



Orb(f, x, 1, 0, 1000)

#Returns first 1000 solutions of the recurrence



#There is a steady state in this reccurence.



#We use the proc SFP to find it.



SFP(f, x);

                              [7.]



#

#Problem 2

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f := x*(1 - x);

                         f := x (1 - x)



Orb(f, x, 0.5, 0, 1000):



g := 2*x*(1 - x);

                        g := 2 x (1 - x)



Orb(g, x, 0.5, 0, 1000):



h := 2.5*x*(1 - x);

                       h := 2.5 x (1 - x)



Orb(h, x, 0.5, 0, 1000):



j := 3.1*x*(1 - x);

                       j := 3.1 x (1 - x)



Orb(j, x, 0.5, 0, 1000):



L := 3.5*x*(1 - x);

                       L := 3.5 x (1 - x)



Orb(L, x, 0.5, 0, 1000):



#We can see from the orbit in these cases whether or not there are stable points. 



#

#Problem 3

#

 p := (x - 1 + 8*(x - 2))/(x - 1 + 9*(x - 2));

                              9 x - 17 

                         p := ---------

                              10 x - 19



Orb(p, x, 0.5, 0, 1000):



SFP(p, x);

                         [0.8900980486]

#There is a stable point