تقرير
Reducible Abelian varieties and Lax matrices for Euler's problem of two fixed centres
| العنوان: | Reducible Abelian varieties and Lax matrices for Euler's problem of two fixed centres |
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| المؤلفون: | Tsiganov, A. V. |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics Mathematical Physics Nonlinear Sciences |
| مصطلحات موضوعية: | Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematical Physics, Mathematics - Dynamical Systems |
| الوصف: | 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 |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1088/1361-6544/ac8a3b |
| URL الوصول: | http://arxiv.org/abs/2104.10362 |
| رقم الأكسشن: | edsarx.2104.10362 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1088/1361-6544/ac8a3b |
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