Publications and Preprints

• (with M. Pollicott) Bowen—Series coding and zeros of the Selberg zeta function; (pdf).
• (with C. Matheus and G. Moreira). On the graph of the dimension function of the Lagrange and Markov spectra, arXiv:2212.11371(pdf).
• (with C. Wormell) Hausdorff dimension of the Apollonian gasket, Inventiones Mathematicae, Vol. 239, pages 909—946, 2025; (pdf).
• (with M. Pollicott). Groups, drift and harmonic measures, with M. Pollicott. In Mathematics going forward — collected mathematical brushstrokes, volume 2313 of Lecture Notes in Math., pp. 301—311. Springer, Cham, 2023; arXiv:2204.08197(pdf).
• (with M. Pollicott). Accurate bounds on Lyapunov exponents for expanding maps of the interval, Communications in Mathematical Physics, vol. 397, pp. 485—502 (2023) (pdf).
• (with C. Matheus, G. Moreira and M. Pollicott). Hausdorff dimension of Gauss--Cantor sets and two applications to classical Lagrange and Markov spectra, Advances in Mathematics, Vol. 409, Part B, paper 108693. (pdf). Code is available on github.
• (with V. Kleptsyn and M. Pollicott) Uniform lower bounds on the dimension of Bernoulli convolutions. Advances in Mathematics, (pdf);  
  Raw data for the plots: Bernoulli convolutions(.dat) and {0,1,3}-system(.dat); Fortran code available on github.
• (with M. Pollicott) Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets of Fuchsian group, Transactions of the AMS, Ser. B, Vol. 9, pp. 1102—1159 (pdf)
• (with O. Jenkinson and M. Pollicott) How many inflections are there in the Lyapunov spectrum? Comm. Math. Phys. 386 (2021), no. 3, 1383—1411; (pdf).
• (with M. Pollicott) Zeros of the Selberg zeta function for non-compact surfaces. Geometriae Dedicata (2019) 201:155—186; (pdf).
• (with O. Jenkinson and M. Pollicott) Rigorous computation of diffusion coefficients for expanding maps. J. Stat. Phys. 170 (2018), no. 2, 221–253. (pdf)
• (with M. Pollicott) Critical points for the Hausdorff dimension of pairs of pants. Groups Geom. Dyn. 11 (2017), no. 4, 1497—1519. (pdf)
• (with M. Pollicott) Linear response and periodic points. Nonlinearity 29 (2016), no. 10, 3047–3066. (pdf)
• (with O. Kozlovski) Fast dynamo on the real plane (preprint). (pdf)
• (with O. Kozlovski) Toy dynamo model on the real line (preprint). (pdf)
• (with M. Pollicott) Estimating singularity dimension. Math. Proc. Cambridge Philos. Soc. 158 (2015), no. 2, 223–238. (pdf)
• (with V. Dremov and G. Shabat) On dynamical systems with 2-adic time. // Proceedings of The Steklov Institute of Mathematics, 2009, Vol. 265, pp. 101–109 (pdf)
• (with V. Dremov and G. Shabat) On the chaotic properties of quadratic maps over non-archimedean fields. // AIP Conf. Proc.— March 29, 2006, Issue 1, pp.43–54 (pdf)