By Cantor Polynomials, we mean the OPs associated to the classical Cantor measure (translated to be
symmetric about zero). We show convincing numerical evidence that the Jacobi parameters are asymptotically
almost periodic. We consider three other families with singular continuous spectrum of zero Lebesgue
measure and likely fractal structure - critical almost Mathieu, Fibonacci and Doubling Julia - and discuss
many open problem problems and a few results for these classes.
This is joint work with Helge Krueger.