Noncanonical time transformations relating finite-dimensional integrable systems
Dual Stäckel systems related by a noncanonical transformation of time variable are considered. Special emphasis is applied to the singularity analysis methods that are used to verify the integrability of the physical model. The properties of some dual integrable systems are investigated and the corresponding Lax pairs and \(z\)-matrix algebras are constructed. Examples of the Kepler problem deformations close to the Drach-type systems, as well as the Holt systems with the second integral of motion of the third or fourth degree in moment \(a\) are studied in details.
scientific article; zbMATH DE number 1465914