The author justifies the reduction principle for the system of weakly nonlinear abstract impulsive equations (1)
) are complex Banach spaces,
. Particularly, the existence of a unique piecewise continuous bounded integral manifold
, which is given by the map
, is established and the integral distance between an arbitrary solution and
is estimated (Theorem 1). This result allows to prove the global strong dynamic equivalence between (1) and some much simpler (decomposed into two parts) impulsive system (Theorem 2).