Bifurcations of the magnetic axis and the alternating-hyperbolic sawtooth

We present a sawtooth model that explains observations where the central safety factor, q 0, stays well below one, which is irreconcilable with current models that predict a reset to q 0 = 1 after the crash. We identify the structure of the field around the magnetic axis with elements of the Lie group SL(2, R)$"SRC="nfab9a0dieqn1.gif"/> and find a transition to an alternating-hyperbolic geometry when q 0 = 2/3. This transition is driven by an ideal MHD instability and leads to a chaotic magnetic field near the axis.