论文标题
理性四维椭圆形的特殊偏心率
Special eccentricities of rational four-dimensional ellipsoids
论文作者
论文摘要
麦克杜夫（McDuff）和施伦克（Schlenk）的惊人结果断言，在确定何时可以将四维符号椭圆形的椭圆形嵌入到四维符号球中时，答案由奇怪的index fibonacci数字和金色平均值确定的“无限楼梯”控制。在这里，我们研究了一个四维符号椭圆形的嵌入到另一个，我们表明，如果目标是理性的，那么McDuff和Schlenk发现的无限楼梯现象非常罕见。具体而言，在合理情况下，精确的三种情况下有一个无限的楼梯 - 当目标具有“偏心率” 1、2或3/2时；在所有其他情况下，答案都是由经典体积障碍物给出的，除非有限的紧凑间隔是线性的。这在Ellipsoid的特殊情况下验证了Holm，Mandini，Pires和作者的猜想。
A striking result of McDuff and Schlenk asserts that in determining when a four-dimensional symplectic ellipsoid can be symplectically embedded into a four-dimensional symplectic ball, the answer is governed by an "infinite staircase" determined by the odd-index Fibonacci numbers and the Golden Mean. Here we study embeddings of one four-dimensional symplectic ellipsoid into another, and we show that if the target is rational, then the infinite staircase phenomenon found by McDuff and Schlenk is quite rare. Specifically, in the rational case, there is an infinite staircase in precisely three cases -- when the target has "eccentricity" 1, 2, or 3/2; in all other cases the answer is given by the classical volume obstruction except on finitely many compact intervals on which it is linear. This verifies in the special case of ellipsoids a conjecture by Holm, Mandini, Pires, and the author.
