Abstract:
In this article, we study a convex embedding for the Euler problem of two fixed centers for energies below the critical energy level. We prove that the doubly-covered elliptic coordinates provide a 2-to-1 symplectic embedding such that the image of the bounded component near the lighter primary of the regularized Euler problem is convex for any energy below the critical Jacobi energy. This holds true if the two primaries have equal mass, but does not hold near the heavier body.
Keywords:
convex embedding, global surface of section, Euler problem of two fixed centers.
\Bibitem{Kim18}
\by Seongchan Kim
\paper On a Convex Embedding of the Euler Problem of Two Fixed Centers
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 3
\pages 304--324
\mathnet{http://mi.mathnet.ru/rcd325}
\crossref{https://doi.org/10.1134/S1560354718030061}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3811821}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2018RCD....23..304K}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048098131}
Linking options:
https://www.mathnet.ru/eng/rcd325
https://www.mathnet.ru/eng/rcd/v23/i3/p304
This publication is cited in the following 2 articles:
Naiara V. de Paulo, Pedro A. S. Salomão, “Reeb flows, pseudo-holomorphic curves and transverse foliations”, São Paulo J. Math. Sci., 16:1 (2022), 314
N. V. de Paulo, P. A. S. Salomao, “On the multiplicity of periodic orbits and homoclinics near critical energy levels of Hamiltonian systems in R-4”, Trans. Am. Math. Soc., 372:2 (2019), 859–887
Citation in format AMSBIB
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