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)
- The growth and distribution of large circles on translation surfaces (with P. Colognese)
- 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)
- Accurate bounds on Lyapunov exponents for expanding maps of the interval (with P. Vytnova)
- Rigidity of pressures of Holder potentials and the fitting of analytic functions to them (with Liangang Ma)
Papers accepted for publication
- Groups, drift and harmonic measures (with P. Vytnova), contribution to a Lecture Notes in Mathematics
- Minimizing entropy for translation surfaces (with P. Colognese), to appear in Conformal Geometry and Dynamics
- Gibbs measures for hyperbolic attractors defined by densities (with D. Parmenter), to appear in Discrete and Continuous Dynamical Systems
- Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets (with P.Vytnova), to appear in Transactions of the American Mathematical Society
- Maximizing measures for Bernoulli measures and the Gauss map to appear in Proceedings of the American Mathematical Society
- Comparison theorems for closed geodesics on negatively curved surfaces (with S. Cantrell), to appear in Groups, Geometry and Dynamics
- An infinite interval version of the alpha-Kakutani equidistribution problem (with B. Sewell), to appear in Israel Journal of Mathematics
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); and Fractal Geometry, notes associated to a lecture course at Warwick.
- 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
- Kneading sequences of triangles and tetrahedra (with P. Colognese) An 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