Giulio Tiozzo - Papers
Dynamics of quadratic polynomials
The core entropy for polynomials of higher degree,
(with Y. Gao), arXiv:1703.08703.
The local Holder exponent for the entropy of real unimodal maps,
Continuity of core entropy of quadratic polynomials,
Inventiones Mathematicae 203 (2016), no. 3, 891-921.
- Topological entropy of quadratic polynomials and dimension of sections of the Mandelbrot set,
Advances in Mathematics 273 (2015), 651-715.
- Galois conjugates of entropies of real unimodal maps,
arXiv:1310.7647 (also check out the related Gallery).
Random walks on groups
Random walks of infinite moment on free semigroups,
(with B. Forghani), arXiv:1712.00860.
Counting problems in graph products and relatively hyperbolic groups,
(with I. Gekhtman, S. Taylor), arXiv:1711.04177.
Counting loxodromics for hyperbolic actions,
(with I. Gekhtman, S. Taylor), arXiv:1605.02103.
- Sublinear deviation between geodesics and sample paths,
Duke Mathematical Journal 164 (2015), no. 3, 511-539.
Random extensions of free groups and surface groups are hyperbolic,
(with S. Taylor), International Mathematics Research Notices IMRN 2016 (2016), no. 1, 294--310.
Random walks on weakly hyperbolic groups,
(with J. Maher), to appear in Journal für die reine und angewandte Mathematik.
- Word length statistics of Teichmueller geodesics and singularity of harmonic measure,
(with V. Gadre, J. Maher), Commentarii Mathematici Helvetici 92 (2017), no. 1, 1--36.
Word length statistics and Lyapunov exponents for Fuchsian groups with cusps,
(with V. Gadre, J. Maher), New York Journal of Mathematics 21 (2015), 511-531.
Dynamics of continued fractions
- A canonical thickening of Q and the entropy of alpha-continued fraction transformations,
(with C. Carminati),
Ergodic Theory and Dynamical Systems 32, no. 4 (2012), 1249-1269.
- Dynamics of continued fractions and kneading sequences of unimodal maps,
(with C. Bonanno, C. Carminati, S. Isola),
Discrete and Continuous Dynamical Systems 33, no. 4 (2013), 1313-1332.
- The entropy of alpha-continued fractions: analytical results,
Annali della Scuola Normale Superiore di Pisa 13 (2014), 1009-1037.
- Tuning and plateaux for the entropy of alpha-continued fractions,
(with C. Carminati), Nonlinearity 26 (2013), 1049-1070.
- The entropy of alpha-continued fractions: numerical results,
(with C. Carminati, S. Marmi, A. Profeti),
Nonlinearity 23 (2010), 2429-2456.
- Continued fractions with SL(2, Z)-branches: combinatorics and entropy,
(with C. Carminati, S. Isola),
to appear in Transactions of the American Mathematical Society.
- The bifurcation locus for numbers of bounded type,
(with C. Carminati), arXiv:1109.0516.
Generalised continuation by means of right limits,
(with D. Sauzin), to appear in Journal d'Analyse Mathématique.
The local Holder exponent for the dimension of invariant
subsets of the circle,
(with C. Carminati), Ergodic Theory and Dynamical Systems 37 (2017), no. 6, 1825-1840.