Smoothness of invariant manifolds for nonautonomous equations
The authors investigate the smoothness of invariant manifolds for nonlinear equations of the form \[ v'=A(t)v+f(t,v) \] with zero solution under the weakest assumption on the linear part \(v' =A(t)v\), namely the existence of a nonuniform exponential dichotomy, e.g., for stable manifolds it is enough to assume that there exist negative Lyapunov exponents. The paper builds on [J. Differ. Equations 221, No.~1, 58--90 (2006; Zbl 1098.34036)] by the authors and proves \(C^1\) smoothness of the invariant manifolds of the trivial solution (cf. also with the authors [Nonlinearity 18, No.~5, 2373--2390 (2005; Zbl 1089.34040)] for higher regularity).
scientific article; zbMATH DE number 5013703