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Proof of a conjecture by H. Dullin and R. Montgomery - MaRDI portal

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Proof of a conjecture by H. Dullin and R. Montgomery

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Publication:6506595

arXiv2209.07097MaRDI QIDQ6506595

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Abstract: We prove a conjecture by H. Dullin and R. Montgomery which states that the two periods of the quasi--periodic motions of the planar Euler problem as well as their ratio, the {it rotation number}, are monotone functions of its non--trivial first integral, at any fixed energy level.\ The proof is based on a link between the Euler and the Kepler problem, which allows for an independent representation of the periods. The theory of real--analytic functions (especially elliptic integrals) is also used.





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