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Published online by Cambridge University Press: 12 April 2016
The properties of the characteristic curves of several families of periodic orbits, in a conservative dynamical system of two degrees of freedom, symmetric with respect to both axes, are reviewed. The two main types of families are presented. One sees that the pattern of the characteristics in the exact resonance case is similar to that of the near resonance case except for the basic characteristic . The form of the characteristics can be found theoretically by means of the second integral.