Church, Kevin E. M.Liu, Xinzhi2018-04-182018-04-182018-04-160022-0396https://doi.org/10.1016/j.jde.2018.04.021http://hdl.handle.net/10012/13105Preprint of an article published in Journal of Differential Equations, available at: https://doi.org/10.1016/j.jde.2018.04.021The existence and smoothness of centre manifolds and a reduction principle are proven for impulsive delay differential equations. Several intermediate results of theoretical interest are developed, including a variation of constants formula for linear equations in the phase space of right-continuous regulated functions, linear variational equation and smoothness of the nonautonomous process, and a Floquet theorem for periodic systems. Three examples are provided to illustrate the results.enCentre manifoldImpulsive delay differential equationLyapunov–Perron methodVariation-of-constants formulaFloquet theoremPreprint