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

Abstract: In this work, we study the dynamics of an impact hybrid system. We built applications called ZDM (Zero Discontinuity Mapping) and PDM (Poincar\'e 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.