Infinite sequence on 2-element alphabet as coordinates of points, determines by unimodal maps

Classification of commutative pairs of surjective maps of interval, one of which is unimodal

“…For example, for the maps g and ψ from Fig. 7 we have that P = {(0, 0); (1,3); (2,6); (3,9); (4, 12)} and Q = {(0, 0); (4, 2); (6,3); (8,4); (10, 5); (12, 6)}. Thus, we cave naturally come to the classification of the commutative piecewise linear pairs g and ψ, where g is unimodal surjective such that g(0) = g(1) = 0.…”

“…We will introduced some methods to find the conjugacy from the tent map to a given unimodal map g. For any continuous unimodal map g, which is topologically conjugated to the tent map, we have defined in [4] a g-decomposition (β i ) i 0 of any point x ∈ [0, 1]. This g-decomposition coincides with v −1 -coordinates expansion of a point for the skew tent map f v in our [5].…”