Universal twinkling exponents for spectral fluctuations associated with mixed chaology

For systems that are neither fully integrable nor fully chaotic, bifurcations of periodic orbits give rise to semiclassically emergent singularities in the fluctuating part N-fl of the energy-level counting function. The bifurcations dominate the spectral moments M-m((h) over bar)= [(N-fl)(2m)] in the limit (h) over bar --> 0. We argue that M-m((h) over bar) similar to const./(h) over bar(nu m), and calculate the twinkling exponents nu(m) as the result of a competition between bifurcations with different codimensions and repetition numbers.