On the shadowing properties for G-processes

This paper is devoted to the investigation of several notions associated with the shadowing behavior of G-processes. We introduce and explore various types of shadowing, including standard shadowing, h-shadowing, limit shadowing, s-limit shadowing, and exponential limit shadowing for G-processes. It is shown that if two G-processes are uniformly conjugate, then the presence of any of these shadowing properties in one implies the same property holds for the other. Moreover, we establish that a finite direct product of G-processes possesses the h-shadowing property if and only if each constituent G-process in the product exhibits this property. The same equivalence also holds for the other types of shadowing considered.