Report
Partial separability and symplectic-Haantjes manifolds
| العنوان: | Partial separability and symplectic-Haantjes manifolds |
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| المؤلفون: | Reyes, Daniel, Tempesta, Piergiulio, Tondo, Giorgio |
| المصدر: | Annali di Matematica Pura e Applicata (2024), published online |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics, Mathematics - Symplectic Geometry, 37J35, 53A45, 70H20 |
| الوصف: | A theory of partial separability for classical Hamiltonian systems is proposed in the context of Haantjes geometry. As a general result, we show that the knowledge of a non-semisimple symplectic-Haantjes manifold for a given Hamiltonian system is sufficient to construct sets of coordinates (called Darboux-Haantjes coordinates) which allow both the partial separability of the associated Hamilton-Jacobi equations and the block-diagonalization of the operators of the corresponding Haantjes algebra. We also introduce a novel class of Hamiltonian systems, characterized by the existence of a generalized St\"ackel matrix, which by construction are partially separable. They widely generalize the known families of partially separable Hamiltonian systems. Our systems can be described in terms of semisimple but non-maximal-rank symplectic-Haantjes manifolds. Comment: 31 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s10231-024-01462-y |
| URL الوصول: | http://arxiv.org/abs/2305.06844 |
| رقم الانضمام: | edsarx.2305.06844 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s10231-024-01462-y |
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