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.
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
\Bibitem{CieFraVan17}
\by Kai Cieliebak, Urs Frauenfelder, Otto van Koert
\paper Periodic Orbits in the Restricted Three-body Problem and Arnold’s $J^+$-invariant
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 4
\pages 408--434
\mathnet{http://mi.mathnet.ru/rcd263}
\crossref{https://doi.org/10.1134/S1560354717040050}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85026877239}
Linking options:
https://www.mathnet.ru/eng/rcd263
https://www.mathnet.ru/eng/rcd/v22/i4/p408
This publication is cited in the following 9 articles:
Airi Takeuchi, Lei Zhao, “Conformal transformations and integrable mechanical billiards”, Advances in Mathematics, 436 (2024), 109411
Yannis Bähni, “On a theorem by Schlenk”, Calc. Var., 63:5 (2024)
KAI CIELIEBAK, URS FRAUENFELDER, LEI ZHAO, “-invariants for planar two-center Stark–Zeeman systems”, Ergod. Th. Dynam. Sys., 43:7 (2023), 2258
Agustin Moreno, Otto van Koert, “Global hypersurfaces of section in the spatial restricted three-body problem”, Nonlinearity, 35:6 (2022), 2920
J. Kim, S. Kim, “J(+)-like invariants of periodic orbits of the second kind in the restricted three-body problem”, J. Topol. Anal., 12:3 (2020), 675–712
E. E. Zotos, A. Perdiou, V. Kalantonis, “Numerical investigation for the dynamics of the planar circular Pluto-Charon system”, Planet Space Sci., 179 (2019), 104718
S. Kim, “On families of periodic orbits in the restricted three-body problem (vol 18, pg 201, 2019)”, Qual. Theor. Dyn. Syst., 18:3 (2019), 1263–1269
S. Kim, “On families of periodic orbits in the restricted three-body problem”, Qual. Theor. Dyn. Syst., 18:1 (2019), 201–232
U. Frauenfelder, L. Zhao, “Existence of either a periodic collisional orbit or infinitely many consecutive collision orbits in the planar circular restricted three-body problem”, Math. Z., 291:1-2 (2019), 215–225
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