تقرير
On the uniqueness of the strictly convex quadrilateral central configuration with a fixed angle
| العنوان: | On the uniqueness of the strictly convex quadrilateral central configuration with a fixed angle |
|---|---|
| المؤلفون: | Liu, Yangshanshan, Zhang, Shiqing |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics, Mathematics - Dynamical Systems, 70F10, 70F15, 37N05 |
| الوصف: | The conjecture of the existence and the uniqueness of the strictly convex quadrilateral central configuration for the Newtonian 4-body problem is one of the most-talked open problems in the study of the classical n-body problems in celestial mechanics. MacMillan and Bartky first gave its general existence in the 1930s and a particular case for its uniqueness. Still, the general case has yet to be solved perfectly since it was considered by Sim'{o} and Yoccoz in the 1980s and was first mentioned by Albouy and Fu in 2008 in the formal publication. Using coordinates of mutual distances and Morse's critical point theory, we give the (at most) uniqueness of the planar strictly convex 4-body central configuration when the angle of one pair of the opposite sides is given. Comment: Proposition 2 and Lemma 1 are incorrect, which are essential to the structure and the main result of this paper. So, we need some time to withdraw it first and then try to revise the manuscript. Thank you! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.02110 |
| رقم الأكسشن: | edsarx.2407.02110 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |