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Various Results

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Part of the Astrophysics and Space Science Library book series (ASSL,volume 443)

Abstract

In the previous chapter and in particular in Sects. 2 and 3, we built our series by assuming that \( C_{1} \) was given a value sometimes greater than and sometimes.

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  • Periodic Solution
  • Periodic Function
  • Arbitrary Constant
  • Real Root
  • Trigonometric Series

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Fig. 1

Notes

  1. 1.

    From Cantor’s recent work we have learned in fact (using his language) that a set can be perfect without being continuous.

  2. 2.

    It is not necessary here to indicate that these values of \( x_{1}^{0} ,\,x_{2}^{0} ,\,n_{1} \) and \( n_{2} \) are those corresponding to the periodic solution being studied; they are not those which we were using above in the discussion of Lindstedt’s method. The ratio \( n_{1} /n_{2} \) is therefore commensurable.

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Correspondence to Henri Poincaré .

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Poincaré, H. (2017). Various Results. In: The Three-Body Problem and the Equations of Dynamics. Astrophysics and Space Science Library, vol 443. Springer, Cham. https://doi.org/10.1007/978-3-319-52899-1_6

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