Alden Walker

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20092026

most citedRoots, Schottky semigroups, and a proof of Bandt's Conjecture

14 citations · 41 across the 15 of their papers we have counts for

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math.DS2026

Entropy and Translation Length in the Ray Graph

Juliette Bavard, Danny Calegari, Alden Walker

Let $Γ$ be the mapping class group of the plane minus a Cantor set, acting on the ray graph $R$ , and for $γ \in Γ$ let $τ (γ)$ denote the translation length of $γ$ on $\mat…

math.DS2026

Laminations and External Angles for Similarity Pairs

Danny Calegari, Alden Walker

A {\em similarity pair} is the dynamical system in $C$ generated by two maps $f : z \to sz - 1$ and $g : z \to sz + 1$ for $∣ s ∣ < 1$ . Associated to the dynamical system is an attrac…

math.DS2018

Extreme points in limit sets

Danny Calegari, Alden Walker

Given an iterated function system of affine dilations with fixed points the vertices of a regular polygon, we characterize which points in the limit set lie on the boundary of its…

math.DS2014★ 14 cited

Roots, Schottky semigroups, and a proof of Bandt's Conjecture

Danny Calegari, Sarah Koch, Alden Walker

In 1985, Barnsley and Harrington defined a ``Mandelbrot Set'' $M$ for pairs of similarities --- this is the set of complex numbers $z$ with $0 < ∣ z ∣ < 1$ for which the limit…

math.DS2011

Ziggurats and rotation numbers

Danny Calegari, Alden Walker

We establish the existence of new rigidity and rationality phenomena in the theory of nonabelian group actions on the circle, and introduce tools to translate questions about the e…