  Context: The central star of the HR 8799 system is a gamma Doradus-type
pulsator. The system harbours four planetary-mass companions detected by direct
imaging, and is a good solar system analogue. The masses of the companions are
not known accurately, because the estimation depends strongly on the age of the
system, which is also not known with sufficient accuracy. Asteroseismic studies
of the star might help to better constrain the age of HR 8799. We organized an
extensive photometric and multi-site spectroscopic observing campaign for
studying the pulsations of the central star.
  Aims: The aim of the present study is to investigate the pulsation properties
of HR 8799 in detail via the ultra-precise 47-d-long nearly continuous
photometry obtained with the MOST space telescope, and to find as many
independent pulsation modes as possible, which is the prerequisite of an
asteroseismic age determination.
  Methods: We carried out Fourier analysis of the wide-band photometric time
series.
  Results: We find that resonance and sudden amplitude changes characterize the
pulsation of HR 8799. The dominant frequency is always at f1 = 1.978 c/d. Many
multiples of one ninth of the dominant frequency appear in the Fourier spectrum
of the MOST data: n/9 f1, where n={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 17,
18}. Our analysis also reveals that many of these peaks show strong amplitude
decrease and phase variations even on the 47-d time-scale. The dependencies
between the pulsation frequencies of HR 8799 make the planned subsequent
asteroseismic analysis rather difficult. We point out some resemblance between
the light curve of HR 8799 and the modulated pulsation light curves of Blazhko
RR Lyrae stars.
