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Bi-shadowing and delay equations. (English) Zbl 0854.34064

Summary: Bi-shadowing is an extension to the concept of shadowing and is usually used in the context of comparing computed trajectories with the true trajectories of a dynamical system in \(\mathbb{R}^n\). Here the concept is defined in a Banach space and is applied to delay equations to give an apparently new result on nonlinear perturbations of linear delay equations. This is essentially a form of robustness with respect to small nonlinear disturbances.

MSC:

34K05 General theory of functional-differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
34K30 Functional-differential equations in abstract spaces
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