Podrobný výpis o publikaci

We suggest one complete and one partial solution to the selected problems presented in the recently published article On Backward Attractors of Interval Maps(Hantakova and Roth (2021) [15]). Specifically we prove a conjecture proposing a characterisation of sets of ss-limit points (i.e. limit points of all accumulation points of backward orbit branches of a specific point) for graph maps. We show that ss-limit sets coincide with Birkhoff centre <(Rec(f))over bar> and that the condition for a point to belong to its ss-limit set is equivalent to belonging to the ss-limit set of an other point. In the second part of the paper we deal with genericity of having all s alpha-limit sets closed and we prove that maps with not all s alpha-limit sets closed are dense in C-0([0,1]), which partially solves an open problem also suggested in the aforementioned article.