Multifractal analysis of the spectral measure of the Thue-Morse sequence: a periodic orbit approach

摘要

The Fourier spectral density of the Thue-Morse sequence is reinterpreted as the invariant measure of a stochastic dynamical system. Based on this fact, its generalized (Renyi) dimension and f (alpha) statistics are calculated with high precision by cycle expansions of spectral determinant and dynamical zeta function. alpha(q) at integer values of q are also computed in an operator scheme and the asymptotic result in the large-q limit is derived.