  Recently, the theory concerning piecewise smooth vector fields (PSVFs for
short) have been undergoing important improvements. In fact, many results
obtained do not have an analogous for smooth vector fields. For example, the
chaoticity of planar PSVFs, which is impossible for the smooth ones. These
differences are generated by the non-uniqueness of trajectory passing through a
point. Inspired by the classical fact that one-dimensional discrete dynamic
systems can produce chaotic behavior, we construct a conjugation between the
shift map and PSVFs. By means of the results obtained and the techniques
employed, a new perspective on the study of PSVFs is brought to light and,
through already established results for discrete dynamic systems, we will be
able to obtain results regarding PSVFs.
