  A number of planet-host stars have been observed to rotate with a period
equal to an integer multiple of the orbital period of their close planet. We
expand this list by analyzing Kepler data of HAT-P-11 and finding a period
ratio of 6:1. In particular, we present evidence for a long-lived spot on the
stellar surface that is eclipsed by the planet in the same position four times,
every sixth transit. We also identify minima in the out-of-transit lightcurve
and confirm that their phase with respect to the stellar rotation is mostly
stationary for the 48-month timeframe of the observations, confirming the
proposed rotation period. For comparison, we apply our methods to Kepler-17 and
confirm the findings of Bonomo & Lanza (2012) that the period ratio is not
exactly 8:1 in that system. Finally, we provide a hypothesis on how
interactions between a star and its planet could possibly result in an observed
commensurability for systems where the stellar differential rotation profile
happens to include a period at some latitude which is commensurable to the
planetary orbit.
