On the Scaling Laws of Higher Order Q{phase Transitions

q{phase transition points in the context of the thermodynamical formalism of dy-namical 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 eld 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 (q) ' ln + a ((q ?q)== a) where the exponent a = 1; 1=2; 1=3 of the bifurcation parameter depends on general properties of the phase transition point. The approach explains the universal features of the scaling behaviour.