New results on orbital resonances.

Area of Science:

• Celestial Mechanics
• Astrophysics
• Dynamical Astronomy

Background:

• Perturbative analyses of planetary resonances often predict divergent resonance widths at extreme eccentricities.
• Conventional methods, including analytical and averaging techniques, may obscure fine resonant structures.

Purpose of the Study:

• To reexamine the nature of resonance width divergences using non-perturbative numerical analyses.
• To reveal hidden fine structures of resonances and understand chaotic dynamics at various eccentricities.

Main Methods:

• Employed non-perturbative numerical analyses utilizing Poincaré sections from a novel perspective.
• Investigated resonance behavior at low, planet-grazing, and high eccentricities.
• Utilized a geometric viewpoint to relate phase space structures to resonant orbit shapes.

Main Results:

• First-order resonances at low eccentricity exhibit asymmetric branches, not diverging widths, with 'low-eccentricity resonant bridges' connecting them.
• Resonance width remains non-divergent at planet-grazing eccentricity.
• Discovered new resonant structures at high eccentricities, involving bifurcations and co-existing phase-shifted resonance zones, leading to partial loss of libration zones to chaos.

Conclusions:

• The study challenges traditional views on resonance width divergences, revealing complex dynamics at low and high eccentricities.
• Non-perturbative methods offer a deeper insight into resonance structures and chaotic transitions.
• Future research should focus on these newly identified structures to advance the understanding of mean motion resonances.