Discrete Dynamical Systems Proof Help.

[goosefrabbas]

1. The problem statement, all variables and given/known data
How many points in ΣN are fixed by σkN?


2. Relevant equations
σkN is the kth iteration of the shift map σN.


3. The attempt at a solution
I'm not sure where to start. I probably just need a hint.

[HallsofIvy]

First, what, exactly, are ΣN and σN? What are their definitions?