Alessia Francesca Guido

arXiv2026

Effective stability estimates close to resonances with applications to rotational dynamics

We consider nearly-integrable Hamiltonian systems defined over a non-resonant domain. In the neighborhood of resonances, we use Nekhoroshev-like estimates to provide effective stability bounds for the action variables over long time. The applicability conditions of these estimates allow some freedom in the choice of parameters. Hence, we develop an optimization algorithm for choosing parameters that maximize the stability time. To further improve the stability estimates, we use perturbation theory to reduce the norm of the perturbing function. We implement this procedure (effective stability estimates and perturbation theory) to analyze the stability of sequences of irrational (Diophantine) frequencies converging to frequencies corresponding to resonances. We consider two applications to models describing problems of rotational dynamics in Celestial Mechanics: the spin-orbit problem, described by a 1D time-dependent Hamiltonian, and the spin-spin-orbit model, described by a 2D time-dependent Hamiltonian. We show stability results for orbits close to the main resonances associated with such models.

math.DS↗

arXiv2026

Arches of chaos, heteroclinic connections of first-order MMRs and the chaotic transport of small bodies in the Sun-Jupiter system

We investigate the heteroclinic connections between stable and unstable manifolds of unstable periodic orbits associated with the most important mean motion resonances (MMRs) in the Sun-Jupiter planar restricted three-body problem. We explicitly compute the stable and unstable manifolds of the unstable periodic orbits associated with the first order interior MMRs 2:1, 3:2, and the exterior MMR 2:3. We also compute short-time FLI maps showing the chaotic saddle structure created by the manifolds of several interior or exterior MMRs other than the 1:1 (co-orbital) resonance. Transits of particles from the exterior to the interior of Jupiter's orbit and vice versa are allowed for Tisserand parameter lesser than 3, and are shown to exist through a variety of heteroclinic channels. Besides the classical ones by Koon et al., we find heteroclinic connections between manifolds of short-period orbits around L3 and periodic orbits of interior or exterior first order MMRs, as well as direct connections between interior and exterior MMR manifolds not involving co-orbital periodic orbits. Through these manifolds and the corresponding FLI ridges, we explain the 'arches-of-chaos' in the asteroid orbital plane (a,e). Chaotic orbits shadowing heteroclinic trajectories exhibit resonance hopping, suggesting links to quasi-Hildas and Jupiter-family comets. Results are obtained in the circular RTBP but persist in the elliptic problem.

astro-ph.EP↗