I was bored in my PDE class today because the teacher was going through the basics of periodic functions which I have already dealt with a bit; then the thought came to me, “What happens when there is a p such that f(x)=f(px) for all x?” Does anyone know anything about these, like are they routinely used in some field or do they have any additional interesting properties?
After working on this for an hour or so, this is what I have found:
even function = -1 geoperiodic function
if g is periodic then f = g(ln(x)) is geo-periodic
if f(x) = f(kx) where k ≠ 1, then f’ isn’t geo-periodic with “period” k