Richard Sharp's Publications

Papers

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

  2. Prime orbit theorems with multi-dimensional constraints for Axiom A flows, Monat. Math. 114, 261-304, (1992). Published version

  3. The correlation of length spectra of two hyperbolic surfaces, Comm. Math. Phys. 153, 423-430, (1993), (with R. Schwartz). Published version

  4. Closed orbits in homology classes for Anosov flows, Ergodic Theory Dyn. Syst. 13, 387-408, (1993). Published version

  5. Rates of recurrence for Zq and Rq extensions of subshifts of finite type, J. London Math. Soc. 49, 401-416, (1994), (with M. Pollicott). Published version

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

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

  8. Growth series for the commutator subgroup, Proc. Amer. Math. Soc. 124, 1329-1335, (1996), (with M. Pollicott). Published version

  9. Large deviations and the distribution of pre-images of rational maps, Comm. Math. Phys. 181, 733-739, (1996), (with M. Pollicott). Preprint Published version

  10. The circle problem on surfaces of variable negative curvature, Monat. Math. 123, 61-70 (1997), (with M. Pollicott). Preprint Published version

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

  12. Poincaré series and zeta functions for surface group actions on R-trees, Math. Zeit. 226, 335-347, (1997), (with M. Pollicott). Preprint Published version

  13. Comparison theorems and orbit counting in hyperbolic geometry, Trans. Amer. Math. Soc. 350, 473-499, (1998), (with M. Pollicott). Preprint Published version

  14. The Manhattan curve and the correlation of length spectra on hyperbolic surfaces, Math. Zeit. 228, 745-750, (1998). Preprint Published version

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

  16. Relative growth series in some hyperbolic groups, Math. Annalen 312, 125-132, (1998). Preprint Published version

  17. Exponential error terms for growth functions on negatively curved surfaces, Amer. J. Math. 120, 1019-1042, (1998), (with M. Pollicott). Preprint Published version

  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, AMS (2001), (with M. Pollicott). Preprint

  19. Error terms for closed orbits of hyperbolic flows, Ergodic Theory Dyn. Syst. 21, 545-562, (2001), (with M. Pollicott). Preprint Published version

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

  21. Closed geodesics and periods of automorphic forms, Advances in Mathematics 160, 205-216, (2001). Preprint Published version

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

  23. Sector estimates for Kleinian groups, Portugaliae Mathematica 58, 461-471, (2001). Preprint

  24. Local limit theorems for free groups, Mathematische Annalen 321, 889-904, (2001). Preprint Published version

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

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

  27. A local limit theorem for closed geodesics and homology, Transactions of the American Mathematical Society 356, 4897-4908, (2004). Preprint Published version

  28. Livsic theorems, maximizing measures and the stable norm, Dynamical Systems: An International Journal 19, 75-88, (2004) (with M. Pollicott). Preprint Published version

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

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

  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). Preprint.

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

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

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

  35. Critical exponents for groups of isometries, Geometriae Dedicata, 125, 63-74, (2007). Preprint Published version

  36. An analogue of Artin reciprocity for closed orbits of skew products, Ergodic Theory & Dynamical Systems 28, 547-552, (2008) (with M. Pollicott). Preprint (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).)

  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). Preprint

  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). Preprint

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

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

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

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

  43. Degeneracy in the length spectrum for metric graphs, Geometriae Dedicata 149, 177-188, (2010). Preprint Published version

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

  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). Preprint

  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). Preprint

  47. Spectral triples and Gibbs measures for expanding maps on Cantor sets, to appear in the Journal of Noncommutative Geometry. Preprint.

  48. Ergodic theorems for actions of hyperbolic groups, to appear in the Proceedings of the American Mathematical Society (with M. Pollicott) Preprint.

  49. Correlations of length spectra for negatively curved manifolds, to appear in Communications in Mathematical Physics (with M. Pollicott) pdf.

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