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Algebra representations through the logistic map
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**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.