  The origin of the conspicuous amplitude and phase modulation of the RR Lyrae
pulsation - known as the Blazhko effect - is still a mystery after more than
100 years of its discovery. With the help of the Kepler space telescope we have
revealed a new and unexpected phenomenon: period doubling in RR Lyr - the
eponym and prototype of its class - as well as in other Kepler Blazhko RR Lyrae
stars. We have found that period doubling is directly connected to the Blazhko
modulation. Furthermore, with hydrodynamic model calculations we have succeeded
in reproducing the period doubling and proved that the root cause of this
effect is a high order resonance (9:2) between the fundamental mode and the 9th
radial overtone, which is a strange mode. We discuss the implications of these
recent findings on our understanding of the century-old Blazhko problem.
