On α-Limit Sets in Lorenz Maps

The aim of this paper is to show that [Formula: see text]-limit sets in Lorenz maps do not have to be completely invariant. This highlights unexpected dynamical behavior in these maps, showing gaps existing in the literature. Similar result is obtained for unimodal maps on [Formula: see text]. On the basis of provided examples, we also present how the performed study on the structure of [Formula: see text]-limit sets is closely connected with the calculation of the topological entropy.