This article is cited in 13 papers

Periodic Orbits in the Restricted Three-body Problem and Arnold’s $J^+$-invariant

Kai Cieliebak^a, Urs Frauenfelder^a, Otto van Koert<sup>b

a</sup> Mathematisches Institut, Universität Augsburg, Universitätsstrasse 14, Augsburg, 86159 Germany
^b Department of Mathematics and Research Institute of Mathematics, Seoul National University, San 56-1, Sillim-dong, Gwanak-gu, Seoul 08826, South Korea

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 behavior.

Keywords: generic immersions into the plane, Arnold’s plane curve invariants, restricted threebody problem.

MSC: 53A04, 57R42, 70F05, 70F07, 05C10

Received: 03.05.2017
Accepted: 26.06.2017

Language: English

DOI: 10.1134/S1560354717040050

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