论文标题
定期解决相对论开普勒问题的解决方案
Periodic solutions to a perturbed relativistic Kepler problem
论文作者
论文摘要
我们考虑一个扰动的相对论开普勒问题\ begin {equation*} \ dfrac {\ Mathrm {d}} {\ Mathrm {d} t} \ left（\ dfrac {m \ dot {x}}} {\ sqrt {\ sqrt {1- | \ dot {x} \ dfrac {x} {| x |^3}+\ varepsilon \，\ nabla_x u（t，t，x），\ qquad x \ in \ in \ mathbb {r}^2 \ setMinus \ setMinus \ \ \ \ \ \ \}，\ end ext {e e e e e e e equip*是第一个变量中的函数$ t $ - 周期性。对于$ \ varepsilon> 0 $很小，我们证明存在带有规定的绕组编号的$ t $周期解决方案，这是由于不易处理的问题而不变的托里（Tori）分叉。
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)=-α\, \dfrac{x}{|x|^3}+\varepsilon \, \nabla_x U(t,x), \qquad x \in \mathbb{R}^2 \setminus \{0\}, \end{equation*} where $m, α> 0$, $c$ 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.
