Toeplitz kneading sequences and adding machines (Q379495)

A combinatorial characterization in terms of the kneading sequence is found for a unimodal map to have an embedded adding machine (meaning that the map restricted to \(\omega(c)\), where \(c\) is the turning point, is topologically conjugate to an adding machine). The main result is that this property is characterized by the kneading sequence being a non-periodic Toeplitz sequence with the `finite time containment property', and in addition unimodal maps are found with Toeplitz kneading sequences that do not have this property.