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This article is cited in 9 scientific papers (total in 9 papers)
Periodic Orbits in the Restricted Three-body Problem and Arnold’s $J^+$-invariant
Kai Cieliebaka, Urs Frauenfeldera, Otto van Koertb a 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.
Received: 03.05.2017 Accepted: 26.06.2017
Citation:
Kai Cieliebak, Urs Frauenfelder, Otto van Koert, “Periodic Orbits in the Restricted Three-body Problem and Arnold’s $J^+$-invariant”, Regul. Chaotic Dyn., 22:4 (2017), 408–434
Linking options:
https://www.mathnet.ru/eng/rcd263 https://www.mathnet.ru/eng/rcd/v22/i4/p408
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