In this talk we will compare three versions of attractors with large (in the sense of Lebesgue measure) basins of attraction: Milnor, statistical, and physical (in the sense of Ilyashenko). The emphasis will be put on typical continuous (i.e. in topology of uniform convergence) dynamical systems on the unit interval. We will go beyond what is known so far about characteristics of these attractors. We will also explain why in the typical family the attractors depends continuously on the map with respect to the Hausdorff metric.

The talk is based on joint work with Magdalena Forys-Krawiec, Jana Hantakowa and Michal Kowalewski