Publications and Preprints

• (with C. Matheus and G. Moreira). On the graph of the dimension function of the Lagrange and Markov spectra, arXiv:2212.11372(pdf).
• (with M. Pollicott). Groups, drift and harmonic measures, 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).
  Raw 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).
• Heuristic analysis of symmetric tori; in Hu H.(ed) ``Statistical Properties of Nonequilibrium Dynamical Systems''; Springer, Singapore (in press); (pdf).
• (with M. Pollicott) Bowen--Series coding and zeros of the Selberg zeta function; in Hu H.(ed) ``Statistical Properties of Nonequilibrium Dynamical Systems''; Springer, Singapore (in press); (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)