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Award ID contains: 2108572

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  1. ; (, Ergodic theory dynamical systems)
    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 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. 
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    Free, publicly-accessible full text available July 30, 2026
  2. ; (, Groups, Geometry, and Dynamics)
    Full Text Available 
  3. ; ; ; (, Duke Mathematical Journal)
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  4. ; (, The bulletin of the London Mathematical Society)
    null (Ed.)
    Accepted Manuscript Full Text Available
  5. ; (, Bulletin of the London Mathematical Society)
    null (Ed.)
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  6. (, Journal of knot theory and its ramifications)
    null (Ed.)
    Accepted Manuscript Full Text Available
  7. ; ; ; ; ; ; (, Journal of Knot Theory and Its Ramifications)
    null (Ed.)
    We improve the upper bound on superbridge index [Formula: see text] in terms of bridge index [Formula: see text] from [Formula: see text] to [Formula: see text]. 
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