New results on orbital resonances

The paper adopts a non-perturbative perihelion Poincaré section with the stroboscopic angle ψ, explicitly relating the conventional resonant angle via φ = (p+1)ψ, and documents two asymmetric branches (pericentric and apocentric) on opposite sides of the nominal resonance, a bona fide separatrix for the apocentric branch that passes through e = 0, finite (non-divergent) widths at planet-grazing eccentricity ecross, coexistence/terminations/re-emergences at high e, and low-e resonant bridges connecting neighboring first-order resonances; all of these are supported by figures and qualitative geometric arguments in the rotating frame . The candidate model independently derives the same qualitative conclusions using a resonant normal form (pendulum model) on the perihelion section, showing φ = (p+1)ψ, identifying the two fixed-point branches, proving non-divergence of widths (with Δa ∼ √(μ e) at low e), justifying finite widths at ecross, and explaining coexistence/branch terminations via twist-map and saddle–center bifurcations. Where the paper is primarily demonstrative and geometric, the model is analytic; their conclusions align.