Small delay inertial manifolds under numerics: A numerical structural stability result (Q700800)

A delay differential equation of the form \[ \dot x(t)=A x(t)+f(x(t))+g(x(t-\varepsilon)) \] is considered, where \(\varepsilon>0, A\in {\mathbb R}^{n\times n}, f,g\in C^2({\mathbb R}^n, {\mathbb R}^n)\). The existence and \(C^2\)-smoothness of a small inertial maifold is shown. It is proved then that on the inertial manifold the dynamics of the original delay differential equation and its Euler discretization with sufficiently small step are topologically equivalent.