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Investigation of periodic orbits in elliptical galaxies using the method of implicit functions

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Existence of periodic orbits inside elliptical galaxies has been investigated. Necessary conditions for regular, small amplitude periodic motion around the center of galaxy have been derived using implicit functions and solved by approximating through Taylor's series. The solution procedure requires to obtain functions of partial derivatives of dependent variables with respect to initial conditions. Derivation of these functions can be accomplished through solving a set of ordinary differential equations by proper choices of associated initial conditions. The results obtained show complete agreement with those obtained through the application of Poincaré-Lindstedt's method.

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Jalali, M.A., Mehri, B. & Pourtakdoust, S.H. Investigation of periodic orbits in elliptical galaxies using the method of implicit functions. Celestial Mech Dyn Astr 63, 271–287 (1995). https://doi.org/10.1007/BF00692291

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Key words

  • Periodic orbits
  • implicit functions
  • elliptical galaxies