Wild attractors of polymodal negative Schwarzian maps (Q1300445)

The authors study the question of existence of a global attractor and decomposing it into minimal attractors, closely related to that of describing \(\omega\)-limit sets of almost all points. To this end they consider piecewise monotone negative Schwarzian maps of an interval. They prove that if a map has an attractor which is a cycle of intervals then at almost every point of this cycle the map has properties similar to the Markov property.