Report
Periodic solutions to a perturbed relativistic Kepler problem
| العنوان: | Periodic solutions to a perturbed relativistic Kepler problem |
|---|---|
| المؤلفون: | Boscaggin, Alberto, Dambrosio, Walter, Feltrin, Guglielmo |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems, 34C25, 70H0B, 70H12, 83A05 |
| الوصف: | We consider a perturbed relativistic Kepler problem \begin{equation*} \dfrac{\mathrm{d}}{\mathrm{d}t}\left(\dfrac{m\dot{x}}{\sqrt{1-|\dot{x}|^2/c^2}}\right)=-\alpha\, \dfrac{x}{|x|^3}+\varepsilon \, \nabla_x U(t,x), \qquad x \in \mathbb{R}^2 \setminus \{0\}, \end{equation*} where $m, \alpha > 0$, $c$ is the speed of light and $U(t,x)$ is a function $T$-periodic in the first variable. For $\varepsilon > 0$ sufficiently small, we prove the existence of $T$-periodic solutions with prescribed winding number, bifurcating from invariant tori of the unperturbed problem. Comment: 21 pages, 2 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2003.03110 |
| رقم الانضمام: | edsarx.2003.03110 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |