Zero Time Discontinuity Mapping (ZDM) and Poincaré Discontinuity Mapping (PDM) in a neighbourhood of a regular grazing point of order 4 in impacting hybrid systems

In this work, we study the dynamics of an impact hybrid system. We built applications called ZDM (Zero Discontinuity Mapping) and PDM (Poincaré Discontinuity Mapping), for points in a neighbourhood of the 4 order regular grazing point, whose objective is to correct the behaviour of flows in the neighbourhood of this points.