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Schubart Solutions in the Charged Collinear Three-Body Problem

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Abstract

In this paper, we study the existence of Schubart-like periodic solutions in a charged collinear three-body problem by applying the notion of turning points and some continuity arguments. We proved the existence of Schubart solutions for the case where the outer particles repel each other.

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References

  1. Atela, P., McLachlan, R.: Global behavior of the charged isosceles three-body problem. Int. J. Bifurc. Chaos 4, 865–884 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  2. Casasayas, J., Nunes, J.: A restricted charged four-body problem. Celest. Mech. Dyn. Astron. 47, 245–266 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  3. Castro Ortega, A., Falconi, M.: Symmetric periodic orbits and Schubart orbits in the charged collinear three-body problem. Qual. Theory Dyn. Syst. 13(2), 181–196 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  4. Castro Ortega, A., Lacomba, E.A.: Non-hyperbolic equilibria in the charged collinear three-body problem. J. Dyn. Differ. Equ. 24, 85–100 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Broucke, R., Walker, D.E.: Numerical explorations of the rectilinear problem of three bodies. Celest. Mech. 21, 73–81 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hénon, M.: A family of periodic orbits of the planar three-body problem, and their stability. Celest. Mech. Dyn. Astron. 13, 267–285 (1976)

    Article  MATH  Google Scholar 

  7. LLibre, J., Pasca, D., Valls, C.: Qualitative study of a charged restricted three-body problem. J. Differ. Equ. 223(3), 326–338 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. McGehee, R.: Triple collision in the collinear three body problem. Invent. Math. 27, 191–227 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  9. Moeckel, R.: A topological existence proof for the Schubart orbits in the collinear three-body problem. Dis. Con. Dyn. Syst. B 10, 609–620 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ouyang, T., Yan, D.: Periodic solutions with alternating singularities in the collinear four-body problem. Celest. Mech. Dyn. Astron. 109, 229–239 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Schubart, J.: Numerische Aufsuchung periodischer Lösungen im Dreikörperproblem. Astron. Nachriften 283, 17–22 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  12. Venturelli, A.: A variational proof of the existence of Von Schubart’s orbit. Dis. Con. Dyn. Syst. B 10, 699–717 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Mansilla, J.E., Vidal, C.: Geometric interpretation for the spectral stability in the charged three-body problem. Celest. Mech. Dyn. Astron. 113, 205–213 (2012)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

The first author is pleased to acknowledge the financial support from DGAPA which allows him a postdoctoral stay in the Department of Mathematics of the Faculty of Sciences, UNAM. The second author acknowledge the partial support from PAPIIT IN111410.

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Authors and Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias, UNAM, C. Universitaria, C.P. 04510, Mexico, D.F., Mexico

    Alberto Castro Ortega & Manuel Falconi

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  1. Alberto Castro Ortega
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  2. Manuel Falconi
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Correspondence to Alberto Castro Ortega.

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Castro Ortega, A., Falconi, M. Schubart Solutions in the Charged Collinear Three-Body Problem. J Dyn Diff Equat 28, 519–532 (2016). https://doi.org/10.1007/s10884-015-9451-0

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  • DOI: https://doi.org/10.1007/s10884-015-9451-0

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