This makes me wonder what are the fixpoints of f(a) = x^a, and whether they are attractive or not. For example if you take x=sqrt(2) then it appears that 2 is a

This makes me wonder what are the fixpoints of f(a) = x^a, and whether they are attractive or not. For example if you take x=sqrt(2) then it appears that 2 is an attractive fixpoint while 4 is a repelling fixpoint.