# Preprints and unpublished material

### Preprints

- How many inflections are there in the Lyapunov spectrum? (with O.Jenkinson and P.Vytnova)
- Comparison theorems for closed geodesics on negatively curved surfaces (with S. Cantrell)
- The Schottky-Klein prime function and counting functions for Fenchel double crosses
- Higher Teichmüller theory for surface groups and shifts of finite type (with R. Sharp)
- Counting geodesic arcs in a fixed conjugacy class on negatively curved surfaces with boundary
- Zeta functions in higher Teichmuller theory (with R. Sharp)
- Fourier multipliers and transfer operators
- A dynamical approach to validated numerics (survey: with O.Jenkinson)

### Papers accepted for publication

- Zeros of the Selberg zeta function for non-compact surfaces (with P. Vytnova), to appear in
*Geoemtriae Dedicata* - Joint spectral radius, sturmian measures, and the finiteness conjecture, (with O.Jenkinson), to appear in
*Ergodic Theory and Dynamical Systems* - Asymptotic counting in conformal dynamical systems (with M.Urbanski), to appear in
*Memoirs of the American Mathematical Society,*volume 947.

- Rigorous dimension estimates for Cantor sets arising in Zaremba theory (with O. Jenkinson), to appear in
*Contemporary Mathematics* - Volume growth for infinite graphs and translation surfaces (with P. Colognese) to appear in
*Contemporary Mathematics*

- Maximizing measures for Bernoulli measures and the Gauss map to appear in
*Proceedings of the American Mathematical Society*

### 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.
- Statistical properties of the Rauzy-Veech-Zorich map A note written for my own education on Rauzy-Veech-Zorich maps.
- 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