Some comments about normal forms under sampling

The paper is a first attempt to characterize how continuous-time normal form structures are transformed under sampling. Two aspects are pointed out: generically with respect to the sampling period, the degree of the normal form cannot increase under sampling; under sampling, a homogeneous continuous-time normal can be transformed under coordinates change into a discrete-time homogeneous normal form. The study is set in the context of differential/difference representations of discrete-time dynamics