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arXiv · 2607.25347

Topological Stability in Paired Dynamical Systems

Abdul Gaffar Khan·Pramod Kumar Das·Tarun Das
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Abstract

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 $g^{-1}f$. 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.

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Abdul Gaffar Khan, Pramod Kumar Das, Tarun Das. 2026-07-28. Topological Stability in Paired Dynamical Systems. https://arxiv.org/abs/2607.25347

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