Institute of Mathematics of NAS of Ukraine,

3 Tereshchenkivs'ka Str.,

01601 Kyiv-4, UKRAINE

E-mail: tanya@imath.kiev.ua, stascon@i.com.ua, yurii_sam@imath.kiev.ua

**On quantum inharmonic oscillator**

**Abstract:**

The *C**-algebras associated with quadratic unimodal maps *f*(*x*)=*ax*(1-*x*)
and *g*(*x*)=1+*ax*-*bx*^{2} are considered.
The later called the algebra of inharmonic quantum oscillator. Representation
theory is developed and the isomorphism invariant under assumption of simplicity
of the dynamical systems is presented.