Published November 25, 2018 | Version v1.0
Software Open

Numerical explorations in a modified potential of the TBP

Authors/Creators

  • 1. Universidad CEU Cardenal Herrera
  • 2. Universidad de Sevilla
  • 3. University of Gent

Description

This is a working document distributed in 2005 among our group and other researchers interested about bifurcation for numerical continuation of modified potential of the three body problem (TBP) starting from the figure-8 Chenciner and Montgomery(2000). In 2018, Dr.~Toshiaki Fujiwara told us that he was going to cite our private communication about this topic. Therefore, this document is making publicly available that communication as well as the code for numerical continuation with AUTO. The body of this document consists in the working document of 2005, adding some remarks as footnotes and a bibliography with the papers where the algorithms are described.

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Additional details

Related works

Is supplement to
https://github.com/fjmalmaraz/continuation-modified-TBP/tree/v1.0 (URL)

References

  • Chenciner, A. & Montgomery, R. (2000). A remarkable periodic solution of the three-body problem in the case of equal masses. Annals of Mathematics-Second Series, 152(3), 881-902.
  • Muñoz-Almaraz, F. J., Freire, E., Galán, J., Doedel, E. & Vanderbauwhede, A. (2003). Continuation of periodic orbits in conservative and Hamiltonian systems. Physica D: Nonlinear Phenomena, 181(1–2), 1–38.
  • Muñoz–Almaraz, F. J., Gal\'an-Vioque, J. & Freire, E. (2004). Families of symmetric periodic orbits in the three body problem and the figure eight. Monografías de La Real Academia de Ciencias de Zaragoza, 25, 229–240.
  • Muñoz-Almaraz, F. J., Freire, E., Galán-Vioque, J. & Vanderbauwhede, A. (2007). Continuation of normal doubly symmetric orbits in conservative reversible systems. Celestial Mechanics and Dynamical Astronomy, 97(1), 17–47.
  • Muñoz–Almaraz, F. J., Freire, E., Galán-Vioque, J. & Vanderbauwhede, A. (2009). Change of Stability without Bifurcation: An Example}. In Proceedings of the 14th International Conference on Difference Equations and Applications (pp. 3–18). Istambul. Turkey: Ugur-Bahcesehir University Publishing.