2026/07/28 by Abdul Gaffar Khan, Pramod Kumar Das, Tarun Das
Mathematics · #math.DS
We study the classical topological dynamical notions of shadowing and topological stability from a viewpoint of paired dynamical system (f,g), where f and g are uniform equivalences on a metric space X. We observe that if g is equicontinuous and commutes with f, then the study of shadowing for (f,g) is reduced to the study of the classical shadowing for g-1f. The fact that these assumptions are sufficient is justified through examples. Finally, we prove that if f is an expansive homeomorphism on a relatively compact metric space, then any pair (f,g) with shadowing is topologically stable.