HW 2 Help

theoldernoah

This is what I have so far for part (a):

[dmath]x_0 = b_1 b_2 \cdots b_{11}\overline{a_1 a_2 \cdots a_7}[/dmath]
with
[dmath]b_5 b_6 \cdots b_{11} \neq a_1 a_2 \cdots a_7.[/dmath]

Am I going in the right direction and how would I represent [imath]x_0[/imath] as a sum?

mark

First, the image with the original longer question is right here . I'd really like to see this stuff typed up, though.

The stuff you had in the original question on the conjugacy looked good. I'm not certain if you knew that you need to compose the two conjugacy functions, though,

To answer the question above, you are absolutely going in the right direction. That second display math equation (an inequality, actually) is particularly astute. You've just got to choose specific zero-one values for the [imath]a[/imath]s and [imath]b[/imath]s.

Lorentz

If I want to land on a specific point after n iterations then would I not have to apply the inverse of the function n times to find a seed value to land on the desired point and if that point has an orbit would the inverse have the same orbit, but reversed for as long as the orbit??
In other news I am having trouble generating a numerical sequence, my cobweb plot seems to indicate an orbit of the desired period, but nestlist on mathematica doesn't seem to like cosines and when I ask for a numerical value nothing changes.

The following loop in python works better for me then using nestlist in mathematica.

x=x_0
for i in range(0,n):
    x=f(x)
    print(x)

mark

@Lorentz

Mathematica works with exact numbers as opposed to decimal approximations by default, thus

Sin[Pi/3]
(* Out: Sqrt[3]/2 *)

but

Sin[Pi/3.0] 
(* Out: 0.866025 *)

Thus, if you want to iterate using decimal approximations, you should set your seed to be a decimal approximation. For example

NestList[Cos, 1.0, 40]
(* Out: 
   {1., 0.540302, 0.857553, 0.65429, 0.79348, 0.701369, 0.76396, 
    0.722102, 0.750418, 0.731404, 0.744237, 0.735605, 0.741425, 0.737507, 
    0.740147, 0.738369, 0.739567, 0.73876, 0.739304, 0.738938, 0.739184, 
    0.739018, 0.73913, 0.739055, 0.739106, 0.739071, 0.739094, 0.739079, 
    0.739089, 0.739082, 0.739087, 0.739084, 0.739086, 0.739085, 0.739086, 
    0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085}
*)

Incidentally, I created those code blocks by simply indenting my input four spaces.