  The first detection of the period doubling phenomenon is reported in the
Kepler RR Lyrae stars RR Lyr, V808 Cyg and V355 Lyr. Interestingly, all these
pulsating stars show Blazhko modulation. The period doubling manifests itself
as alternating maxima and minima of the pulsational cycles in the light curve,
as well as through the appearance of half-integer frequencies located halfway
between the main pulsation period and its harmonics in the frequency spectrum.
The effect was found to be stronger during certain phases of the modulation
cycle. We were able to reproduce the period doubling bifurcation in our
nonlinear RR Lyrae models computed by the Florida-Budapest hydrocode. This
enabled us to trace the origin of this instability in RR Lyrae stars to a
resonance, namely a 9:2 resonance between the fundamental mode and a high-order
(9th) radial overtone showing strange-mode characteristics. We discuss the
connection of this new type of variation to the mysterious Blazhko effect and
argue that it may give us fresh insights to solve this century-old enigma.
