The shape of Thurston's Master Teapot

@article{Bray2021TheSO,
  title={The shape of Thurston's Master Teapot},
  author={Harrison Bray and Diana Davis and Kathryn A. Lindsey and Chenxi Wu},
  journal={Advances in Mathematics},
  year={2021}
}

Figures from this paper

A characterization of Thurston's Master Teapot
We prove an explicit characterization of the points in Thurston's Master Teapot. This description can be implemented algorithmically to test whether a point in $\mathbb{C} \times \mathbb{R}$ belongs
Master Teapots and Entropy Algorithms for the Mandelbrot Set
We construct an analogue of W. Thurston’s “Master teapot" for each principal vein in the Mandelbrot set, and generalize geometric properties known for the corresponding object for real maps. In
Algebraic Number Starscapes
We study the geometry of algebraic numbers in the complex plane, and their Diophantine approximation, aided by extensive computer visualization. Motivated by these images, called algebraic
Accessibility of the Boundary of the Thurston Set
Consider two objects associated to the Iterated Function System (IFS) $\{1+\lambda z,-1+\lambda z\}$: the locus $\mathcal{M}$ of parameters $\lambda\in\mathbb{D}\setminus\{0\}$ for which the
Families of connected self-similar sets generated by complex trees
The theory of complex trees is introduced as a new approach to study a broad class of self-similar sets. Systems of equations encoded by complex trees tip-to-tip equivalence relations are used to
Stability for the 2D MHD equations with horizontal dissipation
In this paper we consider the following 2D MHD system with horizontal dissipation in a strip domain T × R. ∂ t u + u · ∇ u + ∂ 11 u + ∇ p = b · ∇ b , ∂ t b + u · ∇ b + ∂ 11 b = b · ∇ u , ∇ · u = ∇ ·
Polynomials with core entropy zero
TLDR
It is shown that a degree d post-critically finite polynomial f has core entropy zero if and only if f is in the degree d main molecule Md.

References

SHOWING 1-10 OF 52 REFERENCES
“Mandelbrot set” for a pair of linear maps: The local geometry
We consider the iterated function system {λz−1, λz+1} in the complex plane, for λ in the open unit disk. Let M be the set of λ such that the attractor of the IFS is connected. We discuss some
On the Mandelbrot set for pairs of linear maps
A Mandelbrot set for pairs of complex linear maps was introduced by Barnsley and Harrington in 1985. Bousch proved that is locally connected, and Odlyzko and Poonen studied the related set of all
On the ‘Mandelbrot set’ for pairs of linear maps: asymptotic self-similarity
We continue the investigation of iterated function systems (IFS) {λz, λz + 1} in the complex plane, depending on a parameter λ in the open unit disc. Let Aλ be the attractor, and let denote the
On the " Mandelbrot Set " for a Pair of Linear Maps and Complex Bernoulli Convolutions
We consider the family of self-similar sets Aλ, attractors of the iterated function system {C; λz − 1, λz + 1}, depending on a parameter λ in the open unit disk. First we study the set M of those λ
On the `Mandelbrot set' for a pair of linear maps and complex Bernoulli convolutions
We consider the family of self-similar sets A?, attractors of the iterated function system {; ?z?1, ?z+1}, depending on a parameter ? in the open unit disc. First we study the set of those ? for
Hausdorff dimension and biaccessibility for polynomial Julia sets
We investigate the set of biaccessible points for connected polynomial Julia sets of arbitrary degrees $d\geq 2$. We prove that the Hausdorff dimension of the set of external angles corresponding to
Roots, Schottky semigroups, and a proof of Bandt’s conjecture
In 1985, Barnsley and Harrington defined a ‘Mandelbrot Set’ ${\mathcal{M}}$ for pairs of similarities: this is the set of complex numbers $z$ with $0<|z|<1$ for which the limit set of the semigroup
Entropy in Dimension One
This paper completely classifies which numbers arise as the topological entropy associated to postcritically finite self-maps of the unit interval. Specifically, a positive real number h is the
...
...