Reeb’s theorem and periodic orbits for a rotating Hénon

Lanchares, VíctorPascual, Ana IsabelIñarrea, ManuelSalas, José PabloPalacián Subiela, Jesús FranciscoYanguas Sayas, Patricia2020-06-082020-12-0420191572-922210.1007/s10884-019-09814-6https://academica-e.unavarra.es/handle/2454/37101We apply Reeb’s theorem to prove the existence of periodic orbits in the rotating Hénon– Heiles system. To this end, a sort of detuned normal form is calculated that yields a reduced system with at most four non degenerate equilibrium points. Linear stability and bifurcations of equilibrium solutions mimic those for periodic solutions of the original system. We also determine heteroclinic connections that can account for transport phenomena.application/pdfeng© Springer Science+Business Media, LLC, part of Springer Nature 2019AveragingNormalizationReduced spaceHamiltonian oscillatorsPeriodic solutionsReeb’s theorem and periodic orbits for a rotating Hénon–Heiles potentialinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess