Average shadowing and gluing property

Mathematika. 2023. Vol. 69. No. 2. P. 349–365.

Michael Blank

The purpose of this work is threefold: 
(i) extend shadowing theory for discontinuous and non-invertible systems,
(ii) consider more general classes of perturbations (for example, small only on average), 
(iii) establish a general theory based on the property that the shadowing holds 
for the case of a single perturbation. The ``gluing'' construction used in the analysis 
of the last property turns out to be the key point of this theory.

Ключевые слова: динамическая система, dynamical system, pseudo-trajectory, псевдо-траектория, shadowing of pseudo-trajectories, отслеживание