We study the chaotic signatures of the geodesic dynamics of a non-spinning
test particle in the effective-one-body (EOB) formalism for the inspiral
process of spinning binary black holes. We first show that the second order
post-Newtonian (2PN) EOB dynamics is non-integrable by demonstrating that the
EOB metric does not satisfy the criterion for the existence of Carter constant.
We then employ the numerical study to find the plateaus of the rotation curve,
which are associated with the existence of Birkhoff islands in the Poincar\’e
surface of section, signifying the chaotic dynamics in the system. Our results
show the signatures of chaos for the EOB dynamics, especially in the regime of
interest for which the Kerr bounds of the component black holes hold. We also
find that chaotic behavior is more obvious as the spin parameter $a$ of the
deformed EOB background metric increases. Our results can help to uncover the
implications of dynamical chaos in gravitational wave astronomy. Finally, we
also present some preliminary results due to corrections at 3PN order.
