Cieliebak K., Frauenfelder U., van Koert O.
Periodic Orbits in the Restricted Three-body Problem and Arnold’s $J^+$ -invariant
2017, vol. 22, no. 4, pp. 408-434
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.