Chaos in quadratic gravity

While recent gravitational wave observations by LIGO and Virgo allow for tests of general relativity in the extreme gravity regime, these are still blind to a large swath phenomena outside instruments' sensitivity curves. Future gravitational-wave detectors, such as LISA, will enable probes longer-duration lower-frequency events. In particular, LISA characterization non-linear dynamics mass-ratio inspirals, when small compact object falls into supermassive black hole. this paper, we study motion test particles around spinning holes two quadratic theories: scalar Gauss-Bonnet dynamical Chern-Simons gravity. We show that geodesic trajectories rotating theories likely not have fourth constant motion. Poincar\'e sections orbital phase space present chaotic features affect inspiral objects theories. Nevertheless, characteristic size is tiny their location parameter very close event horizon Therefore, detection with challenging, at best.