704 citations · 2.4k across the 64 of their papers we have counts for
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Continued fractions with SL(2, Z)-branches: combinatorics and entropy
Carlo Carminati, Stefano Isola, Giulio Tiozzo
We study the dynamics of a family K_alpha of discontinuous interval maps whose (infinitely many) branches are Moebius transformations in SL(2, Z), and which arise as the critical-l…
Galois conjugates of entropies of real unimodal maps
Giulio Tiozzo
We investigate the set of Galois conjugates of growth rates of superattracting real quadratic polynomials, following W. Thurston. In particular, we prove that the closure of this s…
Topological entropy of quadratic polynomials and dimension of sections of the Mandelbrot set
Giulio Tiozzo
Let c be a real parameter in the Mandelbrot set, and f_c(z):= z^2 + c. We prove a formula relating the topological entropy of f_c to the Hausdorff dimension of the set of rays land…
Generalised continuation by means of right limits
David Sauzin, Giulio Tiozzo
Several theories have been proposed to generalise the concept of analytic continuation to holomorphic functions of the disc for which the circle is a natural boundary. Elaborating…