Here , we will give an independent proof of the existence for inequality ( 2 . 1 . 3 ) , and by the way , give an estimate on the width of the bi - enclosing annulus of closed convex curves in the plane 3 )给出独立的存在性证明,并且还对平面闭凸曲线的bi - enclosing环的宽度给出了一个估计。
In order to prove the existence of the periodic boucing solutions , firstly we will introduce a new coordinate transformation , transform the system from right half plane to the whole plane . and give the relation of the eigenvalues of hill ' s equation and the rotation numbers , using this approach and pioncar - birkhoff twist theorem , we proved the existence of the periodic bouncing solutions for asymptotical linear oscillator 对于周期解的存在性证明,我们引进新的坐标变换把右半平面上的碰撞问题转化到整个平面上,给出旋转数与hill方程的特征值的关系,并以此来度量渐近线性振子,再应用pioncar - birkhoff扭转定理得到周期碰撞解的存在性。