Smooth linearization of nonautonomous difference equations with a nonuniform dichotomy (Q2312832)

The authors provide smooth linearization of nonautonomous difference equations with nonuniform dichotomy. They investigate \(C^{1}\) smooth linearization for nonautonomous difference equation with a nonuniform strong exponential dichotomy. The authors construct a bounded linear operator on a Banach space to convert the linear part of the nonautonomous system to an autonomous one. Then they obtain a gap condition for \(C^{1}\) linearization of such an nonautonomous difference equation and extend the result to compact operators in the finite-dimensional case.