Hausdorff dimension of Gauss-Cantor sets and two applications to classical Lagrange and Markov spectra (with C. Matheus, C. Moreira and P. Vytnova)
- An upper bound on the dimension of the Rauzy gasket (with B. Sewell)
- Minimizing entropy for translation surfaces (with P. Colognese)
- Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets of Fuchsian groups (with P.Vytnova)
Kneading sequences of triangles and tetrahedra (with P. Colognese)
Gibbs measures for hyperbolic attractors defined by densities (with D. Parmenter)
- Comparison theorems for closed geodesics on negatively curved surfaces (with S. Cantrell)
- Counting geodesic arcs in a fixed conjugacy class on negatively curved surfaces with boundary
- Zeta functions in higher Teichmuller theory (with R. Sharp)
- A dynamical approach to validated numerics (survey: with O.Jenkinson)
Papers accepted for publication
- Uniform lower bounds on the dimension of Bernoulli convolutions (with V.Kleptsyn and P.Vytnova), to appear in Advances in Mathematics
- Asymptotic counting in conformal dynamical systems (with M.Urbanski), to appear in Memoirs of the American Mathematical Society, volume 947.
- Maximizing measures for Bernoulli measures and the Gauss map to appear in Proceedings of the American Mathematical Society
- Statistical properties of the Rauzy-Veech-Zorich map (with R.Aimino), to appear in SLN in Math (JM volume)
- Higher Teichmüller theory for surface groups and shifts of finite type (with R. Sharp), to appear in SLN in Math (JM volume)
Surveys and notes from short lecture courses
- Lectures on decay of correlations for flows, Uncorrected notes of lectures given in Jerusalem (1997)
- Lectures on ergodic theory, geodesic flows and related topics, Uncorrected notes of lectures given in Ulm (2003)
- Dynamical zeta functions and closed orbits for geodesic and hyperbolic flows Published survey, Les Houches (2003)
- Fractals and Dimension Theory, Introductory lectures given in Porto (Apr-May, 2005)
- Dynamical Zeta functions, Lectures given in Leiden (June, 2010)
- Dynamical zeta functions and the distribution of orbits, Lectures given in Grenoble (June 2013) [basis of survey to appear in Handbook of Group Actions V]
- Hyperbolic systems, zeta functions and their applications Lectures from Warsaw (2015) [Basis for Survey in Banach Centre Proceedings]
- Lectures on geodesic flows Uncorrected handwritten notes from ESI Vienna (2016)
- Lectures on Bowen-Series method and zeta function Uncorrected handwritten notes from Shenszen (2016) [Basis of survey to be published in proceedings]
- Lectures on fractals and dimension Uncorrected handwritten notes from Tehran (2017)
- Exponential mixing Notes from Mumbai (2017) (handwritten notes) [Basis of survey to be published]
- Apollonius and his circles, appeared in the Notices of the London Mathematical Society
- Lectures on geodesic flows, Lectures from Lisbon (2018)
- Three introductory lectures on Ergodic Theory, Uncorrected handwritten the notes from Bedlewo (2019)
Miscellaneous notes (not intended for publication)
- Limit points for tetrahedra and inscribed spheres An amusing, but elementary, result
- Estimating variance for expanding maps An unfinished note somewhat superceded by newer ideas
- A note on the arcsine law for geodesics A modest distributional result for geodesics
- Formulae for residues of Dynamical Zeta functions A note where the results didn't prove as useful as I hoped.
- Curvature of configuration spaces for planar linkages (with M.L.S. Magalhaes): A longer version of the published article.
- How to create chaos at home (with a 10 second movie and poster ) A poster on how to construct a chaotic linkage.
- Another account of the Dani-Smillie theorem An account I used in my Ergodic Theory course.
- Multiple mixing for hyperbolic flows A project I started (but never finished) during a Sabbatical.
- Large deviations, Gibbs measures and closed geodesics for rank one geodesic flows A modest result now out of date