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A solution to the degree-d twisted rabbit problem
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- Journal:
- Ergodic Theory and Dynamical Systems , First View
- Published online by Cambridge University Press:
- 06 August 2025, pp. 1-16
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We solve generalizations of Hubbard’s twisted rabbit problem for analogs 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 and 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 to a degree-d generalization that depends on the 
$d^2$-adic expansion of the power of the mapping class element by which we twist.
