Preprints

69. Abelian Livsic theorems for Anosov flows, arXiv:2410.17104 pdf

Published and Accepted Papers

68. Distribution in homology classes and discrete fractal dimension, to appear in Proceedings of the Royal Society of Edinburgh Section A: Mathematics (with James Everitt) pdf

67. Distribution of periodic orbits in the homology group of a knot complement, Geometriae Dedicata 218, 75, 2024 (with S. Coles) pdf

66. A non-symmetric Kesten criterion and ratio limit theorem for random walks on amenable groups, International Mathematics Research Notices, volume 2024, issue 7, 6209-6223, 2024 (with R. Dougall) pdf

65. Zeta functions in higher Teichmüller theory, Mathematische Zeitschrift 306, 37, 2024 (with M. Pollicott) pdf

64. Helicity, linking and the distribution of null-homologous periodic orbits for Anosov flows, Nonlinearity 36, 21-58, 2023 (with S. Coles) pdf

63. Statistics of multipliers for hyperbolic rational maps, Discrete and Continuous Dynamical Systems 42, 1225-1241, 2022 (with A. Stylianou) pdf

62. Higher Teichmüller theory for surface groups and shifts of finite type, in "Thermodynamic Formalism" (CIRM Jean-Morlet Chair, Fall 2019), Lecture Notes in Mathematics 2290, Springer-Verlag, 2021 (with M. Pollicott) pdf

61. Relative growth in hyperbolic groups, Monatshefte für Mathematik 195, 1-13, 2021 (with S. Cantrell) pdf

60. A central limit theorem for periodic orbits of hyperbolic flows, Dynamical Systems 36, 142-153, 2021 (with S. Cantrell) pdf

59. Anosov flows, growth rates on covers and group extensions of subshifts, Inventiones mathematicae 223, 445-483, 2021 (with R. Dougall) pdf (Corrigendum correcting an error and filling a gap: Inventiones mathematicae 236, 1505-1509, 2024 pdf)

58. Convergence of zeta functions for amenable group extensions of shifts, in "Dynamics: Topology and Numbers", Contemporary Mathematics 744, 245-257, 2020 pdf

57. Statistics in conjugacy classes in free groups, Geometriae Dedicata 198, 57-70, 2019 (with G. Kenison) pdf

56. Equidistribution of holonomy in homology classes for Anosov flows, Mathematische Zeitschrift 289, 1311-1323, 2018 pdf

55. Orbit counting in conjugacy classes for free groups acting on trees, Journal of Topology and Analysis 9, 631-647, 2017 (with G. Kenison) pdf

54. Amenability, critical exponents of subgroups and growth of closed geodesics, Mathematische Annalen 365, 1359-1377, 2016 (with R. Dougall) pdf

53. Weil-Petersson metrics, Manhattan curves and Hausdorff dimension, Mathematische Zeitschrift 282, 1007-1016, 2016 (with M. Pollicott) pdf

52. Conformal Markov systems, Patterson-Sullivan measure on limit sets and spectral triples, Discrete and Continuous Dynamical Systems 36, 2711-2727, 2016 pdf

51. A Weil-Petersson type metric on spaces of metric graphs, Geometriae Dedicata 172, 229-244, 2014 (with M. Pollicott) pdf

50. Length asymptotics in higher Teichmüller theory, Proceedings of the American Mathematical Society 142, 101-112, 2014 (with M. Pollicott) pdf

49. Correlations of length spectra for negatively curved manifolds, Communications in Mathematical Physics 319, 515-533, 2013 (with M. Pollicott) pdf

48. Ergodic theorems for actions of hyperbolic groups, Proceedings of the American Mathematical Society 141, 1749-1757, 2013 (with M. Pollicott) pdf

47. Spectral triples and Gibbs measures for expanding maps on Cantor sets, Journal of Noncommutative Geometry 6, 801-817, 2012 pdf

46. On the Hannay-Ozorio de Almeida sum formula, in Dynamics, Games and Science II DYNA 2008, 575-590, Springer-Verlag, 2011 (with M. Pollicott) pdf

45. Statistics of matrix products in hyperbolic geometry, in "Dynamical Numbers: Interplay between Dynamical Systems and Number Theory", Contemporary Mathematics 532, 213-230, 2011 (with M. Pollicott) pdf

44. Comparing length functions on free groups, in "Spectrum and Dynamics", CRM Conference Proceedings & Lecture Notes 52, 185-207, 2010 pdf

43. Degeneracy in the length spectrum for metric graphs, Geometriae Dedicata 149, 177-188, 2010 pdf

42. Pairs of periodic orbits with fixed homology difference, Proceedings of Edinburgh Mathematical Society 53, 799-808, 2010 (with M. Risager) pdf

41. Distortion and entropy for automorphisms of free groups, Discrete and Continuous Dynamical Systems 26, 347-363, 2010 pdf

40. Large deviations for intermittent maps, Nonlinearity 22, 2079-2092, 2009 (with M. Pollicott) pdf

39. Large deviations, fluctuations and shrinking intervals, Communications in Mathematical Physics 290, 321-334, 2009 (with M. Pollicott) pdf

38. Lengths, quasi-morphisms and statistics for free groups, in "Spectral Analysis in Geometry and Number Theory" (Dedicated to Toshikazu Sunada on the occasion of his 60th birthday), Contemporary Mathematics 484, 219-237, 2009 (with M. Horsham) pdf

37. Periodic orbits and holonomy for hyperbolic flows, in "Geometric and Probabilistic Structures in Dynamics" (Dedicated to Misha Brin on the occasion of his 60th birthday), Contemporary Mathematics 469, 289-302, 2008 (with M. Pollicott) pdf

36. An analogue of Artin reciprocity for closed orbits of skew products, Ergodic Theory & Dynamical Systems 28, 547-552, 2008 (with M. Pollicott) pdf (Addendum to: W. Parry and M. Pollicott, An analogue of Bauer's Theorem for closed orbits of skew products, Ergodic Theory & Dynamical Systems 28, 535-546, 2008.)

35. Critical exponents for groups of isometries, Geometriae Dedicata, 125, 63-74, 2007 pdf

34. Pseudo-Anosov foliations on periodic surfaces, Topology and its Applications 154, 2365-2375, 2007 (with M. Pollicott) pdf

33. Chebotarev-type theorems in homology classes, Proceedings of the American Mathematical Society, 135, 3887-3894, 2007 (with M. Pollicott) pdf

32. Directions and equidistribution in homology for periodic orbits, Ergodic Theory & Dynamical Systems 27, 405-415, 2007 (with D. Collier) pdf

31. Distribution of ergodic sums for hyperbolic maps, in Representation Theory, Dynamical Systems, and Asymptotic Combinatorics (ed. V. Kaimanovich and A. Lodkin), 167-183, AMS 2006 (with M. Pollicott) pdf

30. Correlations for pairs of closed geodesics, Inventiones mathematicae 163, 1-24, 2006 (with M. Pollicott) pdf

29. Angular self-intersections for closed geodesics on surfaces, Proceedings of the American Mathematical Society 134, 419-426, 2006 (with M. Pollicott) pdf

28. Livsic theorems, maximizing measures and the stable norm, Dynamical Systems 19, 75-88, 2004 (with M. Pollicott) pdf

27. A local limit theorem for closed geodesics and homology, Transactions of the American Mathematical Society 356, 4897-4908, 2004 pdf

26. Uniform estimates for closed geodesics and homology on finite area hyperbolic surfaces, Mathematical Proceedings of the Cambridge Philosophical Society 137, 245-254, 2004 pdf

25. Invariance principles for interval maps with an indifferent fixed point, Communications in Mathematical Physics 229, 337-346, 2002 (with M. Pollicott) pdf

24. Local limit theorems for free groups, Mathematische Annalen 321, 889-904, 2001 pdf

23. Sector estimates for Kleinian groups, Portugaliae Mathematica 58, 461-471, 2001 pdf

22. Asymptotic expansions for closed orbits in homology classes, Geometriae Dedicata 87, 123-160, 2001 (with M. Pollicott) pdf

21. Closed geodesics and periods of automorphic forms, Advances in Mathematics 160, 205-216, 2001 pdf

20. Linear actions of free groups, Annales de l'Institut Fourier 51, 131-150, 2001 (with M. Pollicott) pdf

19. Error terms for closed orbits of hyperbolic flows, Ergodic Theory & Dynamical Systems 21, 545-562, 2001 (with M. Pollicott) pdf

18. Poincaré series and comparison theorems for variable negative curvature, in Topology, Ergodic Theory, Real Algebraic Geometry: Rokhlin's Memorial (ed. V. Turaev and A. Vershik), 229-240, American Mathematical Society, 2001 (with M. Pollicott) pdf

17. Exponential error terms for growth functions on negatively curved surfaces, American Journal of Mathematics 120, 1019-1042, 1998 (with M. Pollicott) pdf

16. Relative growth series in some hyperbolic groups, Mathematische Annalen 312, 125-132, 1998 pdf

15. Large deviations for maps with indifferent fixed points, Nonlinearity 11, 1173-1184, 1998 (with M. Pollicott and M. Yuri) pdf

14. The Manhattan curve and the correlation of length spectra on hyperbolic surfaces, Mathematische Zeitschrift 228, 745-750, 1998 pdf

13. Comparison theorems and orbit counting in hyperbolic geometry, Transactions of the American Mathematical Society 350, 473-499, 1998 (with M. Pollicott) pdf

12. Poincaré series and zeta functions for surface group actions on R-trees, Mathematische Zeitschrift 226, 335-347, 1997 (with M. Pollicott) pdf

11. Growth of periodic points and rotation vectors on surfaces, Topology 36, 765-774, 1997 (with M. Pollicott) pdf

10. The circle problem on surfaces of variable negative curvature, Monatshefte für Mathematik 123, 61-70, 1997 (with M. Pollicott) pdf

9. Large deviations and the distribution of pre-images of rational maps, Communications in Mathematical Physics 181, 733-739, 1996 (with M. Pollicott) pdf

8. Growth series for the commutator subgroup, Proceedings of the American Mathematical Society 124, 1329-1335, 1996 (with M. Pollicott)

7. Periodic points and rotation vectors for torus diffeomorphisms, Topology 34, 351-357, 1995

6. Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature, Inventiones mathematicae 117, 275-302, 1994 (with M. Pollicott)

5. Rates of recurrence for Z^q and R^q extensions of subshifts of finite type, Journal of the London Mathematical Society 49, 401-416, 1994 (with M. Pollicott)

4. Closed orbits in homology classes for Anosov flows, Ergodic Theory & Dynamical Systems 13, 387-408, 1993

3. The correlation of length spectra of two hyperbolic surfaces, Communications in Mathematical Physics 153, 423-430, 1993 (with R. Schwartz)

2. Prime orbit theorems with multi-dimensional constraints for Axiom A flows, Monatshefte für Mathematik 114, 261-304, 1992

1. An analogue of Mertens' theorem for closed orbits of Axiom A flows, Bol. Soc. Bras. Mat. 21, 205-229, 1991

Surveys

Periodic Orbits of Hyperbolic Flows, survey to accompany G. A. Margulis, On Some Aspects of the Theory of Anosov Systems, Springer Monographs in Mathematics, Springer-Verlag, 2004

The mathematical research of William Parry FRS, Ergodic Theory & Dynamical Systems 28, 321-337, 2008 (with M. Pollicott, S. Tuncel and P. Walters)

Notes

Counting in homology: thirty years after, informal notes aimed at making my paper "Closed orbits in homology classes for Anosov flows" more accessible, 2023 pdf

Equidistribution of periodic orbits, note of a mini-course given in the programme "Low-Dimensional Dynamics" at the Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, 2019 pdf

Large deviations for dynamical systems, notes of a mini-course given at International Conference on Statistical Properties of Nonequilibrium Dynamical Systems, SUSTECH, Shenzhen, 2016 pdf