تقرير
Unimodularity and invariant volume forms for Hamiltonian dynamics on Poisson-Lie groups
| العنوان: | Unimodularity and invariant volume forms for Hamiltonian dynamics on Poisson-Lie groups |
|---|---|
| المؤلفون: | Gutierrez-Sagredo, I., Ponte, D. Iglesias, Marrero, J. C., Padrón, E., Ravanpak, Z. |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Mathematical Physics, Mathematics - Dynamical Systems, 37C40, 37J39, 53D17, 70G45, 70H05 |
| الوصف: | In this paper, we discuss several relations between the existence of invariant volume forms for Hamiltonian systems on Poisson-Lie groups and the unimodularity of the Poisson-Lie structure. In particular, we prove that Hamiltonian vector fields on a Lie group endowed with a unimodular Poisson-Lie structure preserve a multiple of any left-invariant volume on the group. Conversely, we also prove that if there exists a Hamiltonian function such that the identity element of the Lie group is a nondegenerate singularity and the associated Hamiltonian vector field preserves a volume form, then the Poisson-Lie structure is necessarily unimodular. Furthermore, we illustrate our theory with different interesting examples, both on semisimple and unimodular Poisson-Lie groups. Comment: 17 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1088/1751-8121/acb116 |
| URL الوصول: | http://arxiv.org/abs/2207.05511 |
| رقم الأكسشن: | edsarx.2207.05511 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1088/1751-8121/acb116 |
|---|