Twisting cubic rabbits
Justin Lanier, Rebecca R. Winarski
TL;DR
This paper generalizes Hubbard's twisted rabbit problem to cubic polynomials, analyzing how twisting by Dehn twists affects the dynamics based on 9-adic expansions, and provides an algorithmic solution for the cubic rabbit case.
Contribution
It introduces a family of twisted polynomial problems extending the twisted rabbit problem to cubic polynomials and offers an algorithmic approach for the cubic rabbit.
Findings
Dependence of twisting results on 9-adic expansion of the twist power
Solution of an infinite family of twisted polynomial problems
Algorithmic method for the cubic rabbit with three post-critical points
Abstract
We solve an infinite family of twisted polynomial problems that are cubic generalizations of Hubbard's twisted rabbit problem. We show how the result of twisting by a power of a certain Dehn twist depends on the 9-adic expansion of the power. For the cubic rabbit with three post-critical points, we also give an algorithmic solution to the twisting problem for the full pure mapping class group.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Advanced Algebra and Geometry