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Award ID contains: 1901247

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  1. ; (, Ergodic Theory and Dynamical Systems)
    Abstract We prove an explicit characterization of the points in Thurston’s Master Teapot, which can be implemented algorithmically to test whether a point in $$\mathbb {C}\times \mathbb {R}$$ belongs to the complement of the Master Teapot. As an application, we show that the intersection of the Master Teapot with the unit cylinder is not symmetrical under reflection through the plane that is the product of the imaginary axis of $$\mathbb {C}$$ and $$\mathbb {R}$$ . 
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  2. ; ; (, International Mathematics Research Notices)
    Abstract Let $$f$$ be a degree $$d$$ bicritical rational map with critical point set $$\mathcal{C}_f$$ and critical value set $$\mathcal{V}_f$$. Using the group $$\textrm{Deck}(f^k)$$ of deck transformations of $f^k$, we show that if $$g$$ is a bicritical rational map that shares an iterate with $$f$$, then $$\mathcal{C}_f = \mathcal{C}_g$$ and $$\mathcal{V}_f = \mathcal{V}_g$$. Using this, we show that if two bicritical rational maps of even degree $$d$$ share an iterate, then they share a second iterate, and both maps belong to the symmetry locus of degree $$d$$ bicritical rational maps. 
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  3. ; (, SIAM Journal on Applied Algebra and Geometry)
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  4. ; ; ; (, Advances in Mathematics)
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