A NOTE ON LOCAL CENTER MANIFOLDS FOR DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

摘要

In this note we consider local invariant manifolds of functional differential equations x'(t) = f (x(t)) representing differential equations with state-dependent delay. Starting with a local center-stable and a local center-unstable manifold of the functional differential equation at a stationary point, we construct, by a straightforward application of the Implicit Mapping Theorem, a local center manifold.