Periodic orbits in the restricted three-body problem and Arnold's $J^{+}$-invariant

Abstract

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 behaviour.

36 Pages, 16 Figures

Cited by in corpus (3)

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• On a Theorem by Schlenk
• Optimal planar immersions of prescribed winding number and Arnold invariants