A solution to the degree-d twisted rabbit problem
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911195701706752 |
|---|---|
| author | Mukundan, Malavika Winarski, Rebecca R. |
| author_facet | Mukundan, Malavika Winarski, Rebecca R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_06099 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A solution to the degree-d twisted rabbit problem Mukundan, Malavika Winarski, Rebecca R. Dynamical Systems Geometric Topology 37F20 (primary) 57M12 (secondary) 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. |
| title | A solution to the degree-d twisted rabbit problem |
| topic | Dynamical Systems Geometric Topology 37F20 (primary) 57M12 (secondary) |
| url | https://arxiv.org/abs/2209.06099 |