Convergence rate for perturbations of Morse-Smale semiflow (Q6074462)

This interesting paper considers autonomous initial value problems for ordinary differential equations \[ \dot u=F_\eta(u),\quad u(0)=u_\eta^0 , \] in \({\mathbb R}^N\) depending on a parameter \(\eta\) from a metric space. Provided they give rise to a dissipative Morse-Smale semiflow, a new method for obtaining the rate of convergence of corresponding attractors is derived as \(\eta\to\eta_0\). This approach applies to regular, as well as to singular perturbations. In case of quasi-linear ordinary differential equations, it is proved that the convergence rate is optimal. Moreover, rates obtained in earlier contributions (for a second order equation) are improved.