scholarly journals Some remarks on symmetric periodic orbits in the restricted three-body problem

2014 ◽  
Vol 34 (12) ◽  
pp. 5229-5245 ◽  
Author(s):  
Jungsoo Kang ◽  
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Symmetric Periodic Orbits ◽  
Three Body

scholarly journals The Omega limit set of a family of chords

2019 ◽  
pp. 1-25 ◽  
Author(s):  
Edward Belbruno ◽  
Urs Frauenfelder ◽  
Otto van Koert
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Limit Behavior ◽  
Limit Set ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Contact Type ◽  
Symmetric Periodic Orbits ◽  
Three Body ◽  
Omega Limit Set

In this paper, we study the limit behavior of a family of chords on compact energy hypersurfaces of a family of Hamiltonians. Under the assumption that the energy hypersurfaces are all of contact type, we give results on the Omega limit set of this family of chords. Roughly speaking, such a family must either end in a degeneracy, in which case it joins another family, or can be continued. This gives a Floer theoretic explanation of the behavior of certain families of symmetric periodic orbits in many well-known problems, including the restricted three-body problem.

Sign in / Sign up

Export Citation Format

Share Document