From the spectrum of dimensions of a fractal invariant measure of a dynamical system one can extract information about the dynamical process that gave rise to the measure. This is equivalent to finding the class of Hamiltonians of an Ising model with a given thermodynamics. © 1987.
J. Feigenbaum, M., Jensen, M. H., & Procaccia, I. (1987). Time ordering and the thermodynamics of strange sets: Theory and experimental tests. Nuclear Physics B (Proceedings Supplements), 2(C), 497–500. https://doi.org/10.1016/0920-5632(87)90035-1