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arXiv · 1704.08568

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

Kai Cieliebak·Urs Frauenfelder·Otto van Koert
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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.

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Kai Cieliebak, Urs Frauenfelder, Otto van Koert. 2017-04-27. Periodic orbits in the restricted three-body problem and Arnold's $J^+$-invariant. https://doi.org/10.1134/s1560354717040050

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