Onset of chaotic gravitational lensing in non-Kerr rotating black holes with quadrupole mass moment

In the electromagnetic channel, chaotic gravitational lensing is a peculiar phenomenon in strong gravitational lensing. In this work, we analyze the properties and emergence of chaotic gravitational lensing in the Manko-Novikov black hole spacetime. Aiming to understand better the underlying physics, we elaborate on the boundaries of the accessible region in terms of the analyses of the contours of the effective potentials. The latter is associated with the two roots of a quadratic equation. In particular, we explore its interplay with ergoregion, which leads to specific features of the effective potentials, such as the emergence of cuspy edge and the formation of {\it pocket}, that serves as a static constraint on the geodesics. Besides, we investigate the properties of the radial and angular accelerations at the turning points in photons' trajectories. Moreover, the accelerations are analyzed, which is argued to provide a kinematic constraint on the geodesics. It is concluded that the onset of the chaotic lensing is crucially related to both constraints, and as a result, an arbitrarily slight deviation in the incident photon is significantly amplified during the course of evolution through an extensive period, demonstrating the complexity in the highly nonlinear deterministic gravitational system.