Next function , the natural numbered iterates are:

So a super-function would be

(*)

For the regular iteration we need to find a fixed point

or

, .

Then (*) looks like:

If we translate along the x-axis we can get

Check:

Edit: It is regular at .

Summary: is the at regular superfunction of , for .

So a super-function would be

(*)

For the regular iteration we need to find a fixed point

or

, .

Then (*) looks like:

If we translate along the x-axis we can get

Check:

Edit: It is regular at .

Summary: is the at regular superfunction of , for .