Discrete Dynamical Systems Proof Help.

goosefrabbas
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Homework Statement


How many points in ΣN are fixed by σkN?


Homework Equations


σkN is the kth iteration of the shift map σN.


The Attempt at a Solution


I'm not sure where to start. I probably just need a hint.
 
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First, what, exactly, are ΣN and σN? What are their definitions?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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