Majstrenko T. Operator algebras associated with simple one-dimentional dynamical systems

The properties of simple dynamical systems which are necessary for description of irreducible representations of corresponding involutive algebras are studied. The a-boundary sets of bilateral orbits of simple dynamical systems are described and the classification of bilateral non-periodic orbits of simple dynamical system generated by U-mapping is given. Complete classification of all irreducible representations of C*-algebras associated with simple dynamical systems generated by U-mapping is presented. For Unharmonical Quantum Oscillator the irreducible representations for some regions of parameter values are described. The criterion of topological conjugacy of simple dynamical systems generated by U-maps is given. The sufficient condition of isomorphism of C*-algebras assosiated with simple dynamical systems generated by U-mappings is proved.