Dynamics of the Hessian transformation

The determinant of the Hessian matrix of a homogeneous polynomial f defines a hypersurface H(f)=0. When f is either a ternary cubic or a binary quartic, H descends to a rational self-map on the moduli space X(1). This talk explores the resulting dynamical systems, showing how they arise from the dynamics of suitable group homomorphisms, and how this dictates their remarkably symmetric structure. 

Joint work with E. Broggini, M. Houben, D. Lazzarini, R. Lolato, F. Pintore, and D. Taufer.