Skip to main content Skip to navigation

Preprints and unpublished material

Preprints

  1. Hausdorff dimension of Gauss-Cantor sets and two applications to classical Lagrange and Markov spectra (with C. Matheus, C. Moreira and P. Vytnova)

  2. An upper bound on the dimension of the Rauzy gasket (with B. Sewell)
  3. The growth and distribution of large circles on translation surfaces (with P. Colognese)
  4. Counting geodesic arcs in a fixed conjugacy class on negatively curved surfaces with boundary
  5. Zeta functions in higher Teichmuller theory (with R. Sharp)
  6. A dynamical approach to validated numerics (survey: with O.Jenkinson)
  7. Accurate bounds on Lyapunov exponents for expanding maps of the interval (with P. Vytnova)
  8. Rigidity of pressures of Holder potentials and the fitting of analytic functions to them (with Liangang Ma)

Papers accepted for publication

Surveys and notes from short lecture courses

  1. Lectures on decay of correlations for flows, Uncorrected notes of lectures given in Jerusalem (1997)
  2. Lectures on ergodic theory, geodesic flows and related topics, Uncorrected notes of lectures given in Ulm (2003)
  3. Dynamical zeta functions and closed orbits for geodesic and hyperbolic flows Published survey, Les Houches (2003)
  4. Fractals and Dimension Theory, Introductory lectures given in Porto (Apr-May, 2005); and Fractal Geometry, notes associated to a lecture course at Warwick.
  5. Dynamical Zeta functions, Lectures given in Leiden (June, 2010)
  6. 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]
  7. Hyperbolic systems, zeta functions and their applications Lectures from Warsaw (2015) [Basis for Survey in Banach Centre Proceedings]
  8. Lectures on geodesic flows Uncorrected handwritten notes from ESI Vienna (2016)
  9. Lectures on Bowen-Series method and zeta function Uncorrected handwritten notes from Shenszen (2016) [Basis of survey to be published in proceedings]
  10. Lectures on fractals and dimension Uncorrected handwritten notes from Tehran (2017)
  11.  Exponential mixing Notes from Mumbai (2017) (handwritten notes) [Basis of survey to be published]
  12. Apollonius and his circles, appeared in the Notices of the London Mathematical Society
  13. Lectures on geodesic flows, Lectures from Lisbon (2018)
  14. Three introductory lectures on Ergodic Theory, Uncorrected handwritten the notes from Bedlewo (2019)

Miscellaneous notes (not intended for publication)

  1. Limit points for tetrahedra and inscribed spheres An amusing, but elementary, result
  2. Kneading sequences of triangles and tetrahedra (with P. Colognese) An elementary result
  3. Estimating variance for expanding maps An unfinished note somewhat superceded by newer ideas
  4. A note on the arcsine law for geodesics A modest distributional result for geodesics
  5. Formulae for residues of Dynamical Zeta functions A note where the results didn't prove as useful as I hoped.
  6. Curvature of configuration spaces for planar linkages (with M.L.S. Magalhaes): A longer version of the published article.
  7. How to create chaos at home (with a 10 second movie and poster ) A poster on how to construct a chaotic linkage.
  8. Another account of the Dani-Smillie theorem An account I used in my Ergodic Theory course.
  9. Multiple mixing for hyperbolic flows A project I started (but never finished) during a Sabbatical.
  10. Large deviations, Gibbs measures and closed geodesics for rank one geodesic flows A modest result now out of date