Stable manifolds for impulsive equations under nonuniform hyperbolicity
The authors construct invariant stable manifolds for impulsive differential equations under sufficiently small perturbations of a linear equation. Compared with former work, there are two novelties: one is that the authors consider the general case of perturbations of nonuniform exponential dichotomies; and the other is that the authors obtain the optimal smoothness of the invariant outside the jumping times. The novelty of the proof is the use of the fiber contraction principle to establish the smoothness of the invariant manifolds. The reviewer thinks that this is an excellent contribution to the topic of stable manifolds for impulsive equations.
scientific article; zbMATH DE number 5833829