Dynamics of typical Baire-1 functions

Let M be the Cantor space or an n-manifold with B1(M,M) the set of Baire-1 self-maps of M. We prove the following:1.For the typical f∈B1(M,M), the maps x⟼ω(x,f) and x⟼τ(x,f) taking x to its ω-limit set and trajectory, respectively, are continuous at a typical point x∈M.2.If s>0, then for the typical (x,f)∈M×B1(M,M), the Hausdorff s-dimensional measure of ω(x,f) is zero.3.If G1 is a residual subset of M, then there is a residual set of points G2⊂M×B1(M,M) all of which generate as their ω-limit set a particular, unique type of adding machine, and if (x,f)∈G2, then ω(x,f)⊂G1.