  Inspirals of stellar mass compact objects into supermassive black holes are
known as extreme mass ratio inspirals. In the simplest approximation, the
motion of the compact object is modeled as a geodesic in the space-time of the
massive black hole with the orbit decaying due to radiated energy and angular
momentum, thus yielding a highly regular inspiral. However, once the spin of
the secondary compact body is taken into account, integrability is broken and
prolonged resonances along with chaotic motion appear.
  We numerically integrate the motion of a spinning test body in the field of a
non-spinning black hole and analyse it using various methods. We show for the
first time that resonances and chaos can be found even for astrophysical values
of spin. On the other hand, we devise a method to analyse the growth of the
resonances, and we conclude that the resonances we observe are only caused by
terms quadratic in spin and will generally stay very small in the
small-mass-ratio limit. Last but not least, we compute gravitational waveforms
by solving numerically the Teukolsky equations in the time-domain and establish
that they carry information on the motion's dynamics. In particular, we show
that the time series of the gravitational wave strain can be used to discern
regular from chaotic motion of the source.
