  We investigate numerically complex dynamical systems where a fixed point is
surrounded by a disk or ball of quasiperiodic orbits, where there is a change
of variables (or conjugacy) that converts the system into a linear map. We
compute this "linearization" (or conjugacy) from knowledge of a single
quasiperiodic trajectory. In our computations of rotation rates of the almost
periodic orbits and Fourier coefficients of the conjugacy, we only use
knowledge of a trajectory, and we do not assume knowledge of the explicit form
of a dynamical system. This problem is called the Babylonian Problem:
determining the characteristics of a quasiperiodic set from a trajectory. Our
computation of rotation rates and Fourier coefficients depends on the very high
speed of our computational method "the weighted Birkhoff average".
