论文标题
QRT地图的三维概括
A three-dimensional generalization of QRT maps
论文作者
论文摘要
我们提出了三维男子式地图的几何结构，该图保留了两支四边形铅笔。地图充当了互动的组成，进而沿第一笔铅笔的四边形的直线发电机作用，并由第二铅笔四边形的交叉点定义。在第一笔铅笔的每个二次中，地图充当二维QRT地图。 虽然这些地图通常具有很高的程度，但我们发现几何条件可以保证该度降低至3个。由两个已知和两个新颖的Kahan型NAMBU系统的分离来说明所得的3度图，其中包括Euler Top和Zhukovski-Volostra grostations tus tur-vernents，gyrsonsone gyrsonsone gyrsonsone gyrsonsone gyrsonsone gyrsonsonemonsone gyrostation。
We propose a geometric construction of three-dimensional birational maps that preserve two pencils of quadrics. The maps act as compositions of involutions, which, in turn, act along the straight line generators of the quadrics of the first pencil and are defined by the intersections with quadrics of the second pencil. On each quadric of the first pencil, the maps act as two-dimensional QRT maps. While these maps are of a pretty high degree in general, we find geometric conditions which guarantee that the degree is reduced to 3. The resulting degree 3 maps are illustrated by two known and two novel Kahan-type discretizations of three-dimensional Nambu systems, including the Euler top and the Zhukovski-Volterra gyrostat with two non-vanishing components of the gyrostatic momentum.
