Regular and Chaotic Dynamics

, Volume 22, Issue 4, pp 408–434 | Cite as

Periodic orbits in the restricted three-body problem and Arnold’s J +-invariant

  • Kai CieliebakEmail author
  • Urs Frauenfelder
  • Otto van Koert


We apply Arnold’s theory of generic smooth plane curves to Stark–Zeeman systems. This is a class of Hamiltonian dynamical systems that describes the dynamics of an electron in an external electric and magnetic field, and includes many systems from celestial mechanics. Based on Arnold’s J +-invariant, we introduce invariants of periodic orbits in planar Stark–Zeeman systems and study their behavior.


generic immersions into the plane Arnold’s plane curve invariants restricted three-body problem 

MSC2010 numbers

53A04 57R42 70F05 70F07 05C10 


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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • Kai Cieliebak
    • 1
    Email author
  • Urs Frauenfelder
    • 1
  • Otto van Koert
    • 2
  1. 1.Mathematisches InstitutUniversität AugsburgAugsburgGermany
  2. 2.Department of Mathematics and Research Institute of MathematicsSeoul National UniversitySeoulSouth Korea

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