论文标题
解决兔子问题的解决方案
A solution to the degree-d twisted rabbit problem
论文作者
论文摘要
我们解决了Hubbard扭曲的兔子问题的概括，用于$ d \ geq 2 $的兔多项式的类似物。扭曲的兔子问题问：当某个二次多项式（称为Douady Rabbit多项式）被映射类群的循环亚组扭曲时，多项式是由此产生的地图等效的（作为生成器的幂的函数）？ Bartholdi（Nekrashevych）给出的原始二次扭曲兔子问题的解决方案取决于我们扭曲的映射类别功率的4-辅助扩展。在本文中，我们提供了一个解决方案，该解决方案取决于我们扭曲的映射类元素的功率的$ d^2 $ addic扩展。
We solve generalizations of Hubbard's twisted rabbit problem for analogues of the rabbit polynomial of degree $d\geq 2$. The twisted rabbit problem asks: when a certain quadratic polynomial, called the Douady Rabbit polynomial, is twisted by a cyclic subgroup of a mapping class group, to which polynomial is the resulting map equivalent (as a function of the power of the generator)? The solution to the original quadratic twisted rabbit problem, given by Bartholdi--Nekrashevych, depended on the 4-adic expansion of the power of the mapping class by which we twist. In this paper, we provide a solution that depends on the $d^2$-adic expansion of the power of the mapping class element by which we twist.
