Abstract
It is shown, that multifractal complex-temperature singularities can play a significant role in the critical strange sets multifractality. These singularities lead to a finite radius of convergence of the real high-temperature expansions and, therefore, to necessity to use a finite-temperature expansions (an analytic continuation). It is shown, using analytic results on multifractality of strange attractors of the baker map and results of numerical computations of the multifractal spectra on all critical points of phase transitions from period-η-tupling to chaos in 1D iterative system (Chinese Phys. Lett.3, 285 (1986) and J. Phys.A25, 589 (1992)) as well as results of a recent numerical simulation of a quantum system with multifractal spectrum (J. Phys.A28, 2717 (1995)), that the finite-temperature expansions give good approximation for the generalized dimensions Dq in a representative interval of q.
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