On a family of Hill's equations in the complex field

Astronomy and Astrophysics – Astronomy

Scientific paper

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Hill Method, Hyperspaces, Variational Principles, Gauss Equation, Hamiltonian Functions, Liapunov Functions

Scientific paper

The variational equation of the periodic solution in an homogeneous potential of degree 2m leads to a family of Hill's equations. Yoshida (1986, 1987) solves these equations by a transformation to the Gauss equation of hypergeometric functions. This family is studied directly for complex t, and in the case m = 2, a detailed description of critical solutions is given.

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