Periodic Orbits and KAM Tori in the Hénon–Heiles Hamiltonian System: The 1: ω Resonance Case

Vidarte J.; Vera-Damián Y.; Mendoza J.; Gonzales W. · AppliedMath (2026) · DOI: 10.3390/appliedmath6090160

Resumen

We prove the existence and determine the linear stability of periodic orbits in the Hénon–Heiles Hamiltonian system under a (Formula presented.) resonance, with (Formula presented.). The analysis combines Lie–Deprit normalization with regular and singular reduction. We also establish the persistence of two-dimensional KAM tori surrounding the linearly stable periodic orbits and derive periodic asymptotic parametrizations in the original variables.

Instituciones: Universidad Nacional Pedro Ruiz Gallo