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>Algebraically closed real geodesics on n-dimensional ellipsoids are
dense in the parameter space and related to hyperelliptic tangential
coverings
【2h】
Algebraically closed real geodesics on n-dimensional ellipsoids are
dense in the parameter space and related to hyperelliptic tangential
coverings
The closedness condition for real geodesics on n-dimensional ellipsoids is ingeneral transcendental in the parameters (semiaxes of the ellipsoid andconstants of motion). We show that it is algebraic in the parameters if andonly if both the real and the imaginary geodesics are closed and wecharacterize such double--periodicity condition via real hyperelliptictangential coverings. We prove the density of algebraically closed geodesics onn-dimensional ellipsoids with respect to the natural topology in the(2n)-dimensional real parameter space. In particular, the approximatingsequence of algebraic closed geodesics on the approximated ellipsoids may bechosen so to share the same values of the length and of the real period vectoras the limiting closed geodesic on the limiting ellipsoid. Finally, for real doubly-periodic geodesics on triaxial ellipsoids, we showhow to evaluate algebraically the period mapping and we present some explicitexamples of families of algebraically closed geodesics.
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