  The RV Tauri stars constitute a small group of classical pulsating stars with
some dozen known members in the Milky Way. The light variation is caused
predominantly by pulsations, but these alone do not explain the full complexity
of the light curves. High quality photometry of RV Tau-type stars is very rare.
DF Cygni is the only member of this class of stars in the original Kepler
field, hence allowing the most accurate photometric investigation of an RV
Tauri star to date. The main goal is to analyse the periodicities of the RV
Tauri-type star DF Cygni by combining four years of high-quality Kepler
photometry with almost half a century of visual data collected by the American
Association of Variable Star Observers. Kepler quarters of data have been
stitched together to minimize the systematic effects of the space data. The
mean levels have been matched with the AAVSO visual data. Both datasets have
been submitted to Fourier and wavelet analyses, while the stability of the main
pulsations has been studied with the O-C method and the analysis of the
time-dependent amplitudes. DF Cygni shows a very rich behaviour on all
time-scales. The slow variation has a period of 779.606 d and it has been
remarkably coherent during the whole time-span of the combined data. On top of
the long-term cycles the pulsations appear with a period of 24.925 d. Both
types of light variation significantly fluctuate in time, with a constantly
changing interplay of amplitude and phase modulations. The long-period change
(i.e. the RVb signature) somewhat resembles the Long Secondary Period (LSP)
phenomenon of the pulsating red giants, whereas the short-period pulsations are
very similar to those of the Cepheid variables. Comparing the pulsation
patterns with the latest models of Type-II Cepheids, we found evidence of
strong non-linear effects directly observable in the Kepler light curve.
