  We search for signs of period doubling in CoRoT RR Lyrae stars. The
occurrence of this dynamical effect in modulated RR Lyrae stars might help us
to gain more information about the mysterious Blazhko effect. The temporal
variability of the additional frequencies in representatives of all subtypes of
RR Lyrae stars is also investigated. We pre-process CoRoT light curves by
applying trend and jump correction and outlier removal. Standard Fourier
technique is used to analyze the frequency content of our targets and follow
the time dependent phenomena. The most comprehensive collection of CoRoT RR
Lyrae stars, including new discoveries is presented and analyzed. We found
alternating maxima and in some cases half-integer frequencies in four CoRoT
Blazhko RR Lyrae stars, as clear signs of the presence of period doubling. This
reinforces that period doubling is an important ingredient to understand the
Blazhko effect - a premise we derived previously from the Kepler RR Lyrae
sample. As expected, period doubling is detectable only for short time
intervals in most modulated RRab stars. Our results show that the temporal
variability of the additional frequencies in all RR Lyrae sub-types is
ubiquitous. The ephemeral nature and the highly variable amplitude of these
variations suggest a complex underlying dynamics of and an intricate interplay
between radial and possibly nonradial modes in RR Lyrae stars. The omnipresence
of additional modes in all types of RR Lyrae - except in non-modulated RRab
stars - implies that asteroseismology of these objects should be feasible in
the near future (Abridged).
