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.