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

Kai Cieliebak; Otto van Koert; Urs Frauenfelder

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

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arxiv 1704.08568 v1 pith:YTR5YTLX submitted 2017-04-27 math.SG math.DSmath.GT

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

Kai Cieliebak , Urs Frauenfelder , Otto van Koert This is my paper

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keywords systemsarnoldinvariantorbitsperiodicstark-zeemanapplybehaviour

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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.

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

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