2025/08/24 by Shirazi, F. Ayatollah Zadeh, Hakimi, E., Hosseini, A. +1
#37B52 #54H15 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2508.17257
In this paper, we introduce and analyze several key dynamical properties-namely shadowing modulo an ideal, expansivity modulo an ideal, and topological stability modulo an ideal-within the framework of uniform transformation semigroups. Given an ideal \mathcal I on semigroup T, we investigate the interplay between these properties in compact Hausdorff transformation semigroup (T,X,\mathfrakX). Our main result establishes that if a compact Hausdorff transformation semigroup exhibits the shadowing property modulo \mathcal I and is expansive modulo \mathcal I then it is also topologically stable modulo \mathcal I. This extends known stability theorems in classical topological dynamics to the setting of ideal-constrained dynamics. Additionally, we explore the relationship between shadowing modulo \mathcal I and the conventional shadowing property.