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For systems that are neither fully integrable nor fully chaotic, bifurcations of periodic orbits give rise to semiclassically emergent singularities in the fluctuating part Nfl of the energy–level counting function. The bifurcations dominate the spectral moments M m ()=⟨ ( N fl ) 2m ⟩ in the limit ħ → 0. We argue that Mm(ħ) ∽ const./ħvm, and calculate the twinkling exponents vm as the result of a competition between bifurcations with different codimensions and repetition numbers.

Universal twinkling exponents for spectral fluctuations associated with mixed chaology