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We consider the finite temperature metal-insulator transition in the halffilled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. Anew method for calculating the Dynamical Mean Field Theory fixpoint surface inthe phase diagram is presented and shown to be free from the convergenceproblems of standard forward recursion. The fixpoint equation is then analyzedusing dynamical systems methods. On the fixpoint surface the eigenspectra ofits Jacobian is used to characterize the hysteresis boundaries of the firstorder transition line and its second order critical end point. The criticalpoint is shown to be a cusp catastrophe in the parameter space, opening apitchfork bifurcation along the first order transition line, while thehysteresis boundaries are shown to be saddle-node bifurcations of two mergingfixpoints. Using Landau theory the properties of the critical end point isdetermined and related to the critical eigenmode of the Jacobian. Our findingsprovide new insights into basic properties of this intensively studiedtransition.

The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition