Algebra representations through the logistic map

Tatyana Maistrenko

Institute of Mathematics Academy of Sciences of Ukraine

Abstract: We consider a class of algebras associated with one-dimentional dynamical systems, given by the logistic map. In particular, this class contains algebras comprising unharmonic quantum oscillator. Hilbert space representations of these algebras are classified through certain orbits of logistic map. The goal of the presentation is to give a description of orbit space of these dynamical systems. Topological conjugacy of the dynamical systems with varying the parameter of nonlinearity is also discussed.