$C*$-Algebras Associated with $F_{2^n }$ Unimodal Dynamical Systems - Maistrenko, T. Yu.; Popovich, S. V. (Ukrains’kyi Matematychnyi Zhurnal, 2001)
We consider $C*$-algebras associated with simple unimodal one-dimensional ambiguous dynamical systems $(f,R)$ with certain special restrictions. For these algebras, we present a complete classification of irreducible representations in Hilbert spaces and describe the dual space. As an example, we consider the one-parameter family $f_{μ}(x) = μx(1 − x)$.