Reducible Abelian varieties and Lax matrices for Euler's problem of two fixed centres

Autor:	Tsiganov, A. V.
Rok vydání:	2021
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems Mathematical Physics Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
DOI:	10.1088/1361-6544/ac8a3b
Popis:	Abel's quadratures for integrable Hamiltonian systems are defined up to a group law of the corresponding Abelian variety $A$. If $A$ is isogenous to a direct product of Abelian varieties $A\cong A_1\times\cdots\times A_k$, the group law can be used to construct various Lax matrices on the factors $A_1,\ldots,A_k$. As an example, we discuss 2-dimensional reducible Abelian variety $A=E_+\times E_-$, which is a product of 1-dimensional varieties $E_\pm$ obtained by Euler in his study of the two fixed centres problem, and the Lax matrices on the factors $E_\pm$. Comment: 13 pages, 2 figures, AMS fonts
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2104.10362 Zobrazit plný text záznamu View this record from Arxiv