Giulio Tiozzo - Papers
Dynamics of quadratic polynomials
-
Continuity of core entropy of quadratic polynomials,
to appear in Inventiones Mathematicae (2015).
- 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
- 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), to appear in International Mathematics Research Notices (2015).
-
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), arXiv:1212.1481.
-
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), arXiv:1312.6845.
- The bifurcation locus for numbers of bounded type,
(with C. Carminati), arXiv:1109.0516.
Other work
-
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), available at arXiv:1410.5761.
Back