Integrable systems on the sphere, ellipsoid and hyperboloid

Autor:	Tsiganov, A. V.
Rok vydání:	2022
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems Mathematical Physics Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	Affine transformations in Euclidean space generates a correspondence between integrable systems on cotangent bundles to the sphere, ellipsoid and hyperboloid embedded in $R^n$. Using this correspondence and the suitable coupling constant transformations we can get real integrals of motion in the hyperboloid case starting with real integrals of motion in the sphere case. We discuss a few such integrable systems with invariants which are cubic, quartic and sextic polynomials in momenta. Comment: LaTeX with AMS fonts, 15 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.08750 Zobrazit plný text záznamu View this record from Arxiv