论文标题
离散时间Euler顶部和相关的3维不同的birational图的几何形状
Geometry of the discrete time Euler top and related 3-dimensional birational maps
论文作者
论文摘要
在本论文中，我们考虑了Hirota和Kimura给出的Euler顶部的离散化。利用保守数量作为实际3空间中的四边形的几何描述，我们发现在相应的铅笔中存在四边形的统治图，以便两个这样的映射的组成描述了离散时间欧拉顶部的迭代。我们进一步表明，这些地图也可以通过复杂的参与，使用Jacobi椭圆函数或实际参与来描述。最后，我们确定了真实参与成为生育图的案例。
In this thesis we consider a discretization of the Euler top given by Hirota und Kimura. Using the geometric description of the conserved quantities as quadrics in real 3-space, we find that there exist maps on rulings of quadrics in the corresponding pencil, such that the composition of two such maps describes iterations of the discrete time Euler top. We further show that these maps can also be described either by complex involutions, using Jacobi elliptic functions, or by real involutions. Finally, we determine the cases where the real involutions become birational maps.
