Work

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

Year: 2026

Type: article

Abstract: We prove the existence and determine the linear stability of periodic orbits in the Hénon–Heiles Hamiltonian system under a 1:ω resonance, with ω≥2. 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.

Source: AppliedMath

DOI: 10.3390/appliedmath6090160

Authors: Jhon Vidarte, Yrina Vera-Damián, Jesús Mendoza, Walter Gonzales

Institutions: Universidad Católica de la Santísima Concepción, Universidad San Sebastián, Universidad Nacional Pedro Ruíz Gallo

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,207

OpenAlex ID: W7213931007

FWCI:

Cites: 23

Cited by:

Related to: 10