Berry, M. V. and Keating, J. P. and Schomerus, H. (2000) Universal twinkling exponents for spectral fluctuations associated with mixed chaology. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 456. p. 1659. ISSN 1364-5021
Abstract
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 Mm(h) = ((Nfl)2m) in the limit h M 0. We argue that Mm(h) ~ const./hvm, and calculate the twinkling exponents vm as the result of a competition between bifurcations with different codimensions and repetition numbers.