The physical origin of the 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 modulated Kepler RR Lyrae stars. We have found that period doubling is directly connected to the Blazhko modulation.
I review the vigorous developments in theoretical modeling of RR Lyrae pulsation that this discovery has recently spurred. I show the importance of high-order radial resonances, three-mode resonances, and the possibility of chaotic RR Lyrae pulsation. I demonstrate that these findings have a profound implication on our understanding of the century-old Blazkho problem, and discuss a new explanation of the Blazhko-enigma that has emerged in the wake of these investigations.
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