2 papers
math.DS2025
A global shadow lemma and logarithm law for geometrically finite Hilbert geometries
Harrison Bray, Giulio Tiozzo
For geometrically finite group actions on hyperbolic metric spaces and under certain assumptions on the growth of parabolic subgroups, we prove a global shadow lemma for Patterson-…
math.DS2024
Master Teapots and Entropy Algorithms for the Mandelbrot Set
Kathryn Lindsey, Giulio Tiozzo, Chenxi Wu
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…