Eventual shadowing property and topological stability for linear systems

Key Points

• To investigate the relationship between the eventual shadowing property and topological stability in linear systems defined on Banach spaces.
• Analysis of expansive linear homeomorphisms on Banach spaces.
• Comparison of properties in finite-dimensional versus infinite-dimensional Banach spaces.
• Every expansive linear homeomorphism with the eventual shadowing property is topologically stable.
• In finite-dimensional Banach spaces, both properties are equivalent.