Periodic orbits associated to Hamiltonian functions of degree four

Carrasco-Olivera, Dante; Uribe, Marco; Vidal, Cláudio

doi:10.1080/14029251.2014.936756

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Averaging method [32,35] is suitable for this purpose. Indeed, it has been extensively used to determine periodic orbits in both non rotating [1,5,6,[18][19][20] and rotating potentials [8,9] and also to establish periodic orbits for system (1), as it is done in [17]. The method is simple to apply, although some times tricky, but, if the system is Hamiltonian, alternative techniques can be used.…”

Section: Introductionmentioning

confidence: 99%

Reeb’s Theorem and Periodic Orbits for a Rotating Hénon–Heiles Potential

et al. 2019

View full text Add to dashboard Cite

We 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.

show abstract