Systèmes Hamiltoniens Intégrables
| المؤلف الرئيسي: | Bouta, Messaouda (Author) |
|---|---|
| مؤلفين آخرين: | Bahayou, Mohamed El Amine (Advisor) |
| التاريخ الميلادي: |
2018
|
| موقع: | ورقلة |
| الصفحات: | 1 - 23 |
| رقم MD: | 1161490 |
| نوع المحتوى: | رسائل جامعية |
| اللغة: | الفرنسية |
| الدرجة العلمية: | رسالة ماجستير |
| الجامعة: | جامعة قاصدي مرباح - ورقلة |
| الكلية: | كلية الرياضيات وعلوم المادة |
| الدولة: | الجزائر |
| قواعد المعلومات: | Dissertations |
| مواضيع: | |
| رابط المحتوى: |
عدد مرات التحميل
8
| المستخلص: |
An hamiltonian system is the given of a triple (M, w, H), where (M, w) is a symplectic manifold (of dimension 2n) and H is a smooth function on M. The system is said to be integrable if there exists a n-uplet F = (f1, f2,…, fn) of first integrals in involution whose differentials are generically independent. Arnold-Liouville’s Theorem asserts that if the moment map F is proper and regular then its fibers are tori (a Lagrangian fibration) and there exist action-angle coordinates that linearize the hamiltonian system. We are interested in the construction of Lagrangian fibrations associated with integrable systems and ideas that are behind the Arnold-Liouville theorem and its demonstration. |
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