Abstract
The q-phase transition points in the context of the thermodynamical formalism of dynamical systems arise via the degeneracy of eigenvalues of the corresponding transfer operator. The scaling behaviour near bifurcation points of dynamical systems is investigated by a mean-field-like expansion for the characteristic equation of this operator. Scaling relations in the vicinity of q-phase-transition points, which are brought about by a doubly (respectively triply) degenerated eigenvalue, are explicitly derived. For the characteristic function (topological pressure) this relation reads phi (q) approximately=ln nu *+ delta a phi ((q-q*)/ delta a) where the exponent a=1, 1/2, 1/3 of the bifurcation parameter delta depends on general properties of the phase-transition point. The approach explains the universal features of the scaling behaviour.
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