Dynamical and Chaotic Structures in the Trans-Neptunian Region: Insights from Resonance Analysis and Diffusion Rates

The trans-Neptunian space, home to numerous small bodies known as trans-Neptunian objects (TNOs), exhibits diverse dynamical behaviors and serves as a valuable probe into the Solar System's history. These TNOs, relics of past dynamical events, reflect significant changes in the positions of the giant planets over time. Our comprehensive survey, using the FAIR method on over 4,000 TNOs from the JPL database, identified several mean-motion resonances (MMRs) with Neptune and characterized resonant behavior through short-term and long-term libration patterns.This region's structure is significantly influenced by celestial mechanical resonances, including MMRs, secular resonances, and the Kozai resonance. Through a large-scale survey employing dynamical maps, we pinpointed key MMRs and assessed their roles using chaotic diffusion and stability time analysis. Chaotic diffusion rates indicate the long-term evolutionary trends and stability times of TNOs, offering insights into the chaotic nature and stability of their orbits. Studying these resonant behaviors and diffusion rates provides a deeper understanding of the past dynamics of the Solar System, including the migration of giant planets and their impact on smaller bodies. This research maps the overall structure of the trans-Neptunian region, refining existing dynamical classifications and contributing to predictions of the Solar System's future evolution.