Invariant manifolds and foliations for quasiperiodic systems (Q1347243)

The authors are concerned with invariant manifolds of the differential equations (1) \(\dot \theta = \omega + \varepsilon \Theta_ 0 (x) + \varepsilon^ 2 \Theta_ 1 (\theta, x, \varepsilon)\), \(\dot x = \varepsilon Ax + \varepsilon R_ 0 (x) + \varepsilon^ 2 R_ 1 (\theta, x, \varepsilon)\), where \(x \in\mathbb{R}^ n\), \(\omega \in\mathbb{R}^ m\), \(\theta \in T^ m\). The functions \(\theta_ 0, \theta_ 1, R_ 0\) and \(R_ 1\) are supposed to be of \(C^ k\) with \(R_ 0 (0) = DR_ 0 (0) = 0\) and \(\varepsilon, \text{Lip} (R_ 0)\) small enough. Using graph-transformation techniques the authors construct \(C^ k\)-smooth center, center-stable and center-unstable manifolds of the system (1). Estimations, assuring \(C^ 0\)-convergence of the invariant manifolds as \(\varepsilon \to 0\), are given too.