Zero time discontinuity mapping (ZDM) and Poincaré discontinuity mapping (PDM) in a neighborhood of a regular grazing point of order 2 k , k ≥ 2 , k ∈ N in impacting hybrid systems. - Maurício Firmino Silva Lima; Tiago Rodrigo Perdigão (Commun. Nonlinear Sci. Numer. Simul., 2026)