Computation of normal form coefficients of cycle bifurcations of maps by algorithmic differentiation

As an alternative to symbolic differentiation (SD) and finite differences (FD) for computing partial derivatives, we have implemented algorithmic differentiation (AD) techniques into the Matlab bifurcation software Cl_MatcontM, http://sourceforge.net/projects/matcont, where we need to compute derivatives of an iterated map, with respect to state variables. We use derivatives up to the fifth order, of the iteration of a map to arbitrary order. The multilinear forms are needed to compute the normal form coefficients of codimension-1 and -2 bifurcation points. Methods based on finite differences are inaccurate for such computations.