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math.DS2021★ 2 cited
Metrics on trees I. The tower algorithm for interval maps
Giulio Tiozzo
We consider Milnor's "tower algorithm" in the space of piecewise monotone maps, an iterative algorithm on the space of metrics which unifies, on the one hand, Thurston's iterative…
math.DS2021
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…
math.DS2021
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-…