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arXiv · 2406.03951

L-shadowing lemma for the Cauchy equation

K. Lee·C. A. Morales
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Abstract

We prove that if the Cauchy problem $\dot{u}=Au$ in a Banach space is hyperbolic, then the problem has the L-shadowing property. Conversely, if the space is finite-dimensional and the L-shadowing property is satisfied, then the problem is hyperbolic. This generalizes a previous result by Ombach \cite{o, o1} for linear homeomorphisms. Some short applications are given.

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K. Lee, C. A. Morales. 2024-06-06. L-shadowing lemma for the Cauchy equation. https://arxiv.org/abs/2406.03951

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