Journal Article

Coles, Solly Thompson and Sharp, Richard (2022) Helicity, linking and the distribution of null-homologous periodic orbits for Anosov flows. Nonlinearity, 36 (1). 21. doi:10.1088/1361-6544/ac9f9d ISSN 0951-7715.

Sharp, Richard and Stylianou, Anastasios (2022) Statistics of multipliers for hyperbolic rational maps. Discrete and Continuous Dynamical Systems A, 42 (3). pp. 1225-1241. doi:10.3934/dcds.2021153 ISSN 1078-0947.

Cantrell, Stephen and Sharp, Richard (2021) Relative growth in hyperbolic groups. Monatshefte fur Mathematik, 195 . pp. 1-13. doi:10.1007/s00605-021-01511-1 ISSN 0026-9255.

Dougall, Rhiannon and Sharp, Richard (2021) Anosov flows, growth rates on covers and group extensions of subshifts. Inventiones Mathematicae, 223 . pp. 445-483. doi:10.1007/s00222-020-00994-3 ISSN 0020-9910.

Cantrell, Stephen and Sharp, Richard (2021) A central limit theorem for periodic orbits of hyperbolic flows. Dynamical Systems, 36 (1). pp. 142-153. doi:10.1080/14689367.2020.1849030 ISSN 1468-9367.

Kenison, George and Sharp, Richard (2019) Statistics in conjugacy classes in free groups. Geometriae Dedicata, 198 . pp. 57-70. doi:10.1007/s10711-018-0329-2 ISSN 0046-5755.

Kenison, George and Sharp, Richard (2019) Statistics in conjugacy classes in free groups. Geometriae Dedicata, 198 (1). pp. 57-70. doi:10.1007/s10711-018-0329-2 ISSN 0046-5755.

Sharp, Richard (2018) Equidistribution of holonomy in homology classes for Anosov flows. Mathematische Zeitschrift, 289 (3-4). pp. 1311-1323. doi:10.1007/s00209-017-2000-2 ISSN 0025-5874.

Kenison, George and Sharp, Richard (2017) Orbit counting in conjugacy classes for free groups acting on trees. Journal of Topology and Analysis, 9 (4). pp. 631-647. doi:10.1142/S1793525317500261 ISSN 1793-7167.

Dougall, Rhiannon and Sharp, Richard (2016) Amenability, critical exponents of subgroups and growth of closed geodesics. Mathematische Annalen, 365 (3-4). pp. 1359-1377. doi:10.1007/s00208-015-1338-1 ISSN 0025-5831.

Pollicott, Mark and Sharp, Richard (2016) Weil–Petersson metrics, Manhattan curves and Hausdorff dimension. Mathematische Zeitschrift, 282 (3-4). pp. 1007-1016. doi:10.1007/s00209-015-1575-8 ISSN 0025-5874.

Sharp, Richard (2016) Conformal Markov systems, Patterson-Sullivan measure on limit sets and spectral triples. Discrete and Continuous Dynamical Systems, 36 (5). pp. 2711-2727. doi:10.3934/dcds.2016.36.2711 ISSN 1078-0947.

Pollicott, Mark and Sharp, Richard (2014) A Weil–Petersson type metric on spaces of metric graphs. Geometriae Dedicata, Volume 172 (Number 1). pp. 229-244. doi:10.1007/s10711-013-9918-2 ISSN 0046-5755.

Pollicott, Mark and Sharp, Richard (2013) Correlations of length spectra for negatively curved manifolds. Communications in Mathematical Physics, Volume 319 (Number 2). pp. 515-533. doi:10.1007/s00220-012-1644-3 ISSN 0010-3616.

Pollicott, Mark and Sharp, Richard (2012) Ergodic theorems for actions of hyperbolic groups. Proceedings of the American Mathematical Society, 141 (5). pp. 1749-1757. doi:10.1090/S0002-9939-2012-11447-9 ISSN 0002-9939.

Sharp, Richard (2012) Spectral triples and Gibbs measures for expanding maps on Cantor sets. Journal of Noncommutative Geometry, Vol.6 (No.4). pp. 801-817. doi:10.4171/JNCG/106 ISSN 1661-6952.

Sharp, Richard (2010) Degeneracy in the length spectrum for metric graphs. Geometriae Dedicata, Vol.149 (No.1). pp. 177-188. doi:10.1007/s10711-010-9475-x ISSN 0046-5755.

Risager, Morten S. and Sharp, Richard (2010) Pairs of periodic orbits with fixed homology difference. Proceedings of the Edinburgh Mathematical Society, Vol.53 (No.3). pp. 799-808. doi:10.1017/S001309150900008X ISSN 0013-0915 .

Pollicott, Mark and Sharp, Richard (2009) Large deviations for intermittent maps. Nonlinearity, Vol.22 (No.9). pp. 2079-2092. doi:10.1088/0951-7715/22/9/001 ISSN 0951-7715.

Pollicott, Mark and Sharp, Richard (2009) Large deviations, fluctuations and shrinking intervals. Communications in Mathematical Physics, Vol.290 (No.1). pp. 321-334. doi:10.1007/s00220-008-0725-9 ISSN 0010-3616.

Sharp, Richard (2009) Distortion and entropy for automorphisms of free groups. Discrete and Continuous Dynamical Systems, Vol.26 (No.1). pp. 347-363. doi:10.3934/dcds.2010.26.347 ISSN 1078-0947.

Sharp, Richard and Horsham, Matthew (2009) Lengths, quasi-morphisms and statistics for free groups. Contemporary Mathematics, Vol.484 . pp. 219-237. ISSN 0271-4132.

Pollicott, Mark and Sharp, Richard (2008) Addendum: an analogue of Artin reciprocity for closed orbits of skew products. Ergodic Theory and Dynamical Systems, Vol.28 (No.2). pp. 547-552. doi:10.1017/S0143385707000569 ISSN 0143-3857.

Pollicott, Mark, Sharp, Richard, Tuncel, S. and Walters, Peter (2008) The mathematical research of William Parry FRS. Ergodic Theory and Dynamical Systems, Vol.28 (No.2). pp. 321-337. doi:10.1017/S0143385708000102 ISSN 0143-3857.

Pollicott, Mark and Sharp, Richard (2007) Pseudo-Anosov foliations on periodic surfaces. Topology and its Applications, Vol.154 (No.12). pp. 2365-2375. doi:10.1016/j.topol.2007.01.021 ISSN 0166-8641.

Pollicott, Mark and Sharp, Richard (2007) Chebotarev-type theorems in homology classes. Proceedings of the American Mathematical Society, Vol.135 (No.12). pp. 3887-3894. doi:10.1090/S0002-9939-07-08923-X ISSN 0002-9939.

Book Item

Pollicott, Mark and Sharp, Richard (2021) Higher Teichmüller theory for surface groups and shifts of finite type. In: Pollicott, M. and Vaienti, S., (eds.) Thermodynamic Formalism. Lecture Notes in Mathematics, 2290 . Cham: Springer, pp. 395-418. ISBN 9783030748623

Pollicott, Mark and Sharp, Richard (2011) On the Hannay–Ozorio De Almeida sum formula. In: Peixoto, Mauricio Matos and Pinto, Alberto Adrego and Rand, D. A. (David A.), (eds.) Dynamics, Games and Science II. Springer Proceedings in Mathematics, Vol.2 . Berlin ; Heidelberg: Springer, pp. 575-590. ISBN 9783642147876

Conference Item

Sharp, Richard (2010) Comparing length functions on free group. In: Spectrum and Dynamics Workshop, Montreal, Canada, 7-11 Apr 2008. Published in: Spectrum and Dynamics: Proceedings of the Workshop Held in Montréal, QC, April 7-11, 2008: CRM Proceedings & Lecture Notes, Vol.52 pp. 185-207. ISBN 9780821847787.

Pollicott, Mark and Sharp, Richard (2010) Statistics of matrix products in hyperbolic geometry. In: International Conference on Dynamical Numbers: Interplay Between Dynamical systems and Number Theory, Max Planck Inst, Bonn, Germany, 20-24 Jun 2009 . Published in: Dynamical Numbers: Interplay Between Dynamical Systems and Number Theory , Volume 532 pp. 213-230. ISSN 0271-4132.

Pollicott, Mark and Sharp, Richard (2008) Periodic orbits and holonomy for hyperbolic flows. In: Workshop on Dynamical Systems and Related Topics, Univ Maryland, College Pk, MD, Mar 15-18, 2008. Published in: Contemporary Mathematics, Volume 469 pp. 289-302. ISBN 978-0-8218-4286-7. ISSN 0271-4132.