Integrable problems of Euler and Jacobi are not topologically conjugate
Two remarkable integrable systems are considered: the geodesic flow of an ellipsoid (Jacobi problem) and the rotation of a rigid body about its center of mass (Euler problem). Both systems are three parametric: the Jacobi problem is determined by the squares of semiaxes \(a\), \(b\), \(c\) and the Euler problem is determined by the principal moments of inertia \(1/A\), \(1/B\), \(1/C\). In this paper it is proved that for \(a<b<c\) and \(A<B<C\) these systems are not topologically conjugate. This statement must be combined with the results of \textit{A. V. Bolsinov} and \textit{A. T. Fomenko} [Russ. Acad. Sci., Dokl. Math. 50, No. 3, 412-417 (1994); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk 339, No. 3, 293-296 (1994; Zbl 0872.58036)].
scientific article; zbMATH DE number 1564398