Average shadowing revisited

Abstract

We propose a novel unifying approach to study the shadowing property for a broad class of dynamical systems (in particular, discontinuous and non-invertible) under a variety of perturbations. In distinction to known constructions, our approach is local: it is based on the gluing property which takes into account the shadowing under a single (not necessarily small) perturbation.

19 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2202.13407