Songs developing a lag as they progress

If you don't see Unicode data in right-hand sidebar, under your chosen glyph's Name, then you need to add Unicode to your list of categories on the left sidebar.

1. At the top left, click the Gear icon [it always looks greyed-out until you click it]

2. Select Customise List…

3. Scroll down the Select Categories list, open Code Tables & check Unicode.

[I've composited this picture, you won't really see both menus at once]

4. Click Done & click any other glyph to make your new information display.

Hint: Notice $$\frac{-1}{2^n} \leq\frac{\cos^2 n}{ 2^n} \leq \frac{1}{2^n} $$ for all $n$. Now use Squeeze Rule.

A wealth of information is provided in the answers to this question. In particlar, in the paper of Parris cited in the accepted answer, there are number theoretic conditions on $n,$ which guarantee that an action of $\mathbb{Z}/n\mathbb{Z}$ has fixed points.