Authors: | Jovanović, Božidar | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | The Jacobi-Rosochatius Problem on an Ellipsoid: The Lax Representations and Billiards | Journal: | Archive for Rational Mechanics and Analysis | Volume: | 210 | Issue: | 1 | First page: | 101 | Last page: | 131 | Issue Date: | 1-Oct-2013 | Rank: | M21a | ISSN: | 0003-9527 | DOI: | 10.1007/s00205-013-0638-4 | Abstract: | In this article, we construct the Lax representations of the geodesic flow, the Jacobi-Rosochatius problem and its perturbations by means of separable polynomial potentials on an ellipsoid. We prove complete integrability in the case of a generic symmetric ellipsoid and describe analogous systems on complex projective spaces. Also, we consider billiards within an ellipsoid under the influence of the Hook and Rosochatius potentials between the impacts. A geometric interpretation of the integrability analogous to the classical Chasles and Poncelet theorems is given. |
Publisher: | Springer Link |
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