704 citations · 2.4k across the 64 of their papers we have counts for
4 papers · 2 filters
Generalizations of Douady's magic formula
Adam Epstein, Giulio Tiozzo
We generalize a combinatorial formula of Douady from the main cardioid to other hyperbolic components of the Mandelbrot set, constructing an explicit piecewise linear map which…
Thermodynamic formalism for coarse expanding dynamical systems
Tushar Das, Feliks Przytycki, Giulio Tiozzo +2
We consider a class of dynamical systems, which we call weakly coarse expanding, which is a generalization to the postcritically infinite case of expanding Thurston maps as discuss…
Entropy and drift for Gibbs measures on geometrically finite manifolds
Ilya Gekhtman, Giulio Tiozzo
We prove a generalization of the fundamental inequality of Guivarc'h relating entropy, drift and critical exponent to Gibbs measures on geometrically finite quotients of CAT(-1) me…
Cusp excursion in hyperbolic manifolds and singularity of harmonic measure
Anja Randecker, Giulio Tiozzo
We generalize the notion of cusp excursion of geodesic rays by introducing for any the excursion in the cusps of a hyperbolic -manifold of finite volume. We…