Stability of asymptotically stable sets for continuous functions
The paper deals with the problem of the behavior of asymptotically stable sets of \(f \in C(I,I)\), \(I\) a real compact interval, under small perturbations of \(f\). Let \(A(f)\) be the collection of all asymptotically stable sets of \(f\). Consider the map \(\overline A\) defined in \(C(I,I)\) so that \(\overline A(f)\) is the closure of \(A(f)\). It is shown that \(\overline A\) is lower semicontinuous at a residual set of functions in \(C(I,I)\).
scientific article; zbMATH DE number 1866746