Constraining the orbit of the retrograde planet in the $\nu$ Octantis system
The $\nu$ Octantis system is composed of a compact stellar binary and a retrograde S-type planet orbiting near the edge of stability. Here, we investigate the dynamically viable architectures of this system by exploring the planetary orbital elements with a Monte Carlo method. To handle the large number of free parameters, we employed a novel approach in which all relevant orbital parameters were varied simultaneously, which we refer to as corner stability maps. Furthermore, since the osculating orbital period of the planet undergoes large oscillations, we combined these maps with frequency analysis to identify the stable configurations that remain consistent with the observational data. We find that the retrograde planetary orbit most likely lies in the region of influence of the high-order 28/$-$11 mean-motion resonance, where its long-term stability is enhanced by secular apsidal alignment.