论文标题
三个多项式和有理功能的新正常形式
New Normal Forms For Degree Three Polynomials and Rational Functions
论文作者
论文摘要
在动态系统的模量空间中研究家庭时，为共轭类选择适当的代表性功能可能是一项微妙的任务。与代表的定义多项式的合理性相比，最微妙的问题围绕着共轭类别的理性。我们给出了三个多项式的正常形式，该形式具有固定点集等于固定点乘数集的属性。这种正常形式是根据模量空间不变的，因此具有不错的理性属性。我们进一步分类了所有三个理性地图，这些图可以共轭以在固定点和固定点乘数之间具有相似的关系。
When studying families in the moduli space of dynamical systems, choosing an appropriate representative function for a conjugacy class can be a delicate task. The most delicate questions surround rationality of the conjugacy class compared to rationality of the defining polynomials of the representation. We give a normal form for degree three polynomials which has the property that the set of fixed points is equal to the set of fixed point multipliers. This normal form is given in terms of moduli space invariants and, hence, has nice rationality properties. We further classify all degree three rational maps which can be conjugated to have a similar relationship between the fixed points and the fixed point multipliers.
