
Symmetry in Nonlinear Mathematical Physics  2009
Alexandre Gavrilik (Bogolyubov Institute for Theoretical Physics, Kyiv, Ukraine)
QuasiFibonacci oscillators
Abstract:
Diverse classes of nonstandard deformed oscillators are explored
from the viewpoint whether their energy spectra obey (or not) the familiar
Fibonacci relation, whose two coefficients are some constants. The concept
of quasiFibonacci relation/property is developed and shown to be the only
possibility in the case of socalled μdeformed or (μ;p,q)deformed
oscillators. For some other classes of deformed oscillators, three
different variants of extending the Fibonacci property are proven to
exist.

