论文标题
用nilpotent线性部分的地图的正常形式
Normal form for maps with nilpotent linear part
论文作者
论文摘要
使用SL2代理理论确定具有不可约合nilpotent线性部分的N维图的正常形式。我们通过示例绘制如何以算法方式处理可简化的情况。 nilpotent线性部分的SL2三重构造（和证明）比人们希望的要复杂得多，但是一旦抽象SL2理论到位，对正常形式的描述和计算分解以计算坐标转换的生成器，可以在无液位的知识的情况下明确处理。如果一个人希望一个人可以计算正常形式，以便保证它位于操作员的内核中，并且可以确定这确实是相对于nilpotent线性部分的正常形式；可以说明正常形式为SL2式。尽管乍一看，地图的正常形式理论比nilpotent情况下的矢量场更为复杂，但事实证明，最终结果要好得多。如果在矢量场情况下，当一个人要描述正常形式的一般形式时，则在尺寸变大时会遇到不变的理论问题，对于地图，我们可以获得结果而没有对维度的任何限制。据我们所知，在文献中，仅描述了二维nilpotent案例。
The normal form for an n-dimensional map with irreducible nilpotent linear part is determined using sl2-representation theory. We sketch by example how the reducible case can also be treated in an algorithmic manner. The construction (and proof) of the sl2-triple from the nilpotent linear part is more complicated than one would hope for, but once the abstract sl2 theory is in place, both the description of the normal form and the computational splitting to compute the generator of the coordinate transformation can be handled explicitly in terms of the nilpotent linear part without the explicit knowledge of the triple. If one wishes one can compute the normal form such that it is guaranteed to lie in the kernel of an operator and one can be sure that this is really a normal form with respect to the nilpotent linear part; one can state that the normal form is in sl2-style. Although at first sight the normal form theory for maps is more complicated than for vector fields in the nilpotent case, it turns out that the final result is much better. Where in the vector field case one runs into invariant theoretical problems when the dimension gets larger if one wants to describe the general form of the normal form, for maps we obtain results without any restrictions on the dimension. In the literature only the 2-dimensional nilpotent case has been described sofar, as far as we know.
