> #ATTENDANCE QUIZ FOR LECTURE 9 of Dr. Z.'s Math336 Rutgers University # Please
> Edit this .txt page with Answers #Email ShaloshBEkhad@gmail.com #Subject: p9
> #with an attachment called #p9FirstLast.txt #(e.g. p9DoronZeilberger.txt)
> #Right after attending the lecture, but no later than 4:00pm that day #LIST
> ALL THE ATTENDANCE QUESTIONS FOLLOWED BY THEIR ANSWERS
> #Question 1: Using maple, find the fixed points of the mapping x--> 3.6x. If
> it exists (ii) the stable fixing points.
> #I used the functions supplied in the file M9.txt FP:=proc(f,x)
> evalf([solve(f=x)]): end: SFP:=proc(f,x) local L,i,f1,pt,Ls: L:=FP(f,x): #The
> list of fixed points (including complex ones) Ls:=[]: #Ls is the list of
> stable fixed points, that starts out as the empty list f1:=diff(f,x): #The
> derivative of the function f w.r.t. x for i from 1 to nops(L) do pt:=L[i]: if
> abs(subs(x=pt,f1))<1 then Ls:=[op(Ls),pt]: # if pt, is stable we add it to the
> list of stable points fi: od: Ls: #The last line is the output end:
> #Part i FP(3*x,x)
                                     [0.]

> #Part ii SFP(3*x,x)
                                      []

> #There are seemingly no Stable Fixed Points which makes sense as F'(x) would
> be 3, and for no x value is the absolute value of that less than 1 (which is
> the critereon for being stable.
> 
> #Question 2: What other constant did feingenbaum discover and what was the
> significance behind it? #Answer: Feigenbaum discovered both the bifurcation
> constant 4.669201609102990671853203820466 which is the limiting ratio of each
> bifurcation interval, and his other constant was the ratio between the
> branches of a bifurcation diagram which is alpha or
> 2.50290787509589282228390287321