Bondarenko A. Representations of *-algebras connected with piecewise linear-fractional mappings.

The thesis is devoted to the investigations of algebras with an involution by operators in Hilbert space. The classification of irreducible representations by bounded operators was obtained for C*-algebras connected with simple dynamical systems generated by unimodal piecewise linear-fractional mappings. The conditions of existence of attracting cycles were given for dynamical systems generated by piecewise linear-fractional mappings of interval. The П-partitions of dynamical systems were introduced and for any point x in X the description of bilateral orbits of dynamical system (X,f) passing this point was given. Minimal П-partitions are described for unimodal mappings. With the help of these results the method of description of the set of anti-Fock representations of *-algebras generated by the relation XX*=f(X*X) was constructed. Sets of anti-Fock representations of C*-algebras connected with a class of piecewise linear-fractional mappings are described under condition of existence of attractingcycle.