Dynamics of typical Baire-1 functions on a compact $${{\varvec{n}}}$$n-manifold

The simplest erasing substitution

“…Then, {C x } x∈D ∪{1} is a countable closed covering of [0, 1] with the wanted oscillation bound. Indeed, in all cases, we have O R (C x ) 1/2 −1 < ε by (18).…”

“…In this connection, the study of the dynamics of real maps generated by erasing block substitutions appears as a natural development, as the objects constructed in this way fall into a category which is in a way the direct generalisation of the ones cited above, that is Baire class 1, generally not Darboux functions. The systematic investigation of the dynamical properties of these maps has just begun; for instance, generic interval maps of Baire class 1 are studied in [18,36,37].…”