Parameterized shadowing for nonautonomous dynamics

Abstract

For nonautonomous and nonlinear differential and difference equations depending on a parameter, we formulate sufficient conditions under which they exhibit $C^k$, $k\in \mathbb{N}$ 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.