  We study the problem of preservation of maximal canards for time discretized
fast-slow systems with canard fold points. In order to ensure such
preservation, certain favorable structure preserving properties of the
discretization scheme are required. Conventional schemes do not possess such
properties. We perform a detailed analysis for an unconventional discretization
scheme due to Kahan. The analysis uses the blow-up method to deal with the loss
of normal hyperbolicity at the canard point. We show that the structure
preserving properties of the Kahan discretization for quadratic vector fields
imply a similar result as in continuous time, guaranteeing the occurrence of
maximal canards between attracting and repelling slow manifolds upon variation
of a bifurcation parameter. The proof is based on a Melnikov computation along
an invariant separating curve, which organizes the dynamics of the map
similarly to the ODE problem.
