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Parameterized shadowing for nonautonomous dynamics (2302.12603v1)
Published 24 Feb 2023 in math.DS
Abstract: For nonautonomous and nonlinear differential and difference equations depending on a parameter, we formulate sufficient conditions under which they exhibit $Ck$, $k\in \N$ shadowing with respect to a parameter. Our results are applicable to situations when the linear part is not hyperbolic. In the case when the linear part is hyperbolic, we obtain results dealing with parameterized Hyers-Ulam stability.