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

Growth of resonances and chaos for a spinning test particle in the Schwarzschild background