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arXiv · 2209.06099

A solution to the degree-d twisted rabbit problem

Malavika Mukundan·Rebecca R. Winarski
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Abstract

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.

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Malavika Mukundan, Rebecca R. Winarski. 2022-09-13. A solution to the degree-d twisted rabbit problem. https://doi.org/10.1017/etds.2025.137

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