  We obtain the exact solution of the one-loop mode-coupling equations for the
dynamical structure function in the framework of non-linear fluctuating
hydrodynamics in one space dimension for the strictly hyperbolic case where all
characteristic velocities are different. All solutions are characterized by
dynamical exponents which are Kepler ratios of consecutive Fibonacci numbers,
which includes the golden mean as a limiting case. The scaling form of all
higher Fibonacci modes are asymmetric L\'evy-distributions. Thus a hierarchy of
new dynamical universality classes is established. We also compute the precise
numerical value of the Pr\"ahofer-Spohn scaling constant to which scaling
functions obtained from mode coupling theory are sensitive.
