Richard Sharp

Richard Sharp is a British mathematician whose research focuses on dynamical systems and ergodic theory, particularly in the study of geodesic flows on negatively curved manifolds and related areas (such as thermodynamic formalism). He has served as a faculty member at the University of Warwick in the UK, publishing widely on topics involving geometric dynamics and measure-theoretic properties of flows.

All published works

Action	Title	Year	Authors
+ PDF Chat	Distribution of periodic orbits in the homology group of a knot complement	2024	Solly Coles Richard Sharp
+ PDF Chat	Correction to “Anosov flows, growth rates on covers and group extensions of subshifts”	2024	Rhiannon Dougall Richard Sharp
+ PDF Chat	A Non-Symmetric Kesten Criterion and Ratio Limit Theorem for Random Walks on Amenable Groups	2024	Rhiannon Dougall Richard Sharp
+ PDF Chat	Zeta functions in higher Teichmüller theory	2024	Mark Pollicott Richard Sharp
+ PDF Chat	Helicity, linking and the distribution of null-homologous periodic orbits for Anosov flows*	2022	Solly Coles Richard Sharp
+ PDF Chat	Statistics of multipliers for hyperbolic rational maps	2021	Richard Sharp Anastasios Stylianou
+ PDF Chat	Relative Growth in Hyperbolic Groups	2021	Stephen Cantrell Richard Sharp
+ PDF Chat	A central limit theorem for periodic orbits of hyperbolic flows	2021	Stephen Cantrell Richard Sharp
+ PDF Chat	Higher Teichmüller Theory for Surface Groups and Shifts of Finite Type	2021	Mark Pollicott Richard Sharp
+	Statistics of multipliers for hyperbolic rational maps	2020	Richard Sharp Anastasios Stylianou
+ PDF Chat	Anosov flows, growth rates on covers and group extensions of subshifts	2020	Rhiannon Dougall Richard Sharp
+ PDF Chat	Convergence of zeta functions for amenable group extensions of shifts	2020	Richard Sharp
+	Relative growth in hyperbolic groups	2019	Stephen Cantrell Richard Sharp
+	Anosov flows, growth rates on covers and group extensions of subshifts.	2019	Rhiannon Dougall Richard Sharp
+	A Central Limit Theorem for Periodic Orbits of Hyperbolic Flows	2018	Stephen Cantrell Richard Sharp
+ PDF Chat	Statistics in conjugacy classes in free groups	2018	George Kenison Richard Sharp
+ PDF Chat	Equidistribution of holonomy in homology classes for Anosov flows	2017	Richard Sharp
+	Statistics in conjugacy classes in free groups	2017	George Kenison Richard Sharp
+ PDF Chat	Orbit counting in conjugacy classes for free groups acting on trees	2016	George Kenison Richard Sharp
+ PDF Chat	Amenability, critical exponents of subgroups and growth of closed geodesics	2015	Rhiannon Dougall Richard Sharp
+ PDF Chat	Weil–Petersson metrics, Manhattan curves and Hausdorff dimension	2015	Mark Pollicott Richard Sharp
+ PDF Chat	Conformal Markov systems, Patterson-Sullivan measure on limit sets and spectral triples	2015	Richard Sharp
+	Orbit counting in conjugacy classes for free groups acting on trees	2015	George Kenison Richard Sharp
+	Amenability, Critical Exponents of Subgroups and Growth of Closed Geodesics	2014	Rhiannon Dougall Richard Sharp
+	A Weil–Petersson type metric on spaces of metric graphs	2013	Mark Pollicott Richard Sharp
+	Length asymptotics in higher Teichmüller theory	2013	Mark Pollicott Richard Sharp
+	Correlations of Length Spectra for Negatively Curved Manifolds	2012	Mark Pollicott Richard Sharp
+	Ergodic theorems for actions of hyperbolic groups	2012	Mark Pollicott Richard Sharp
+ PDF Chat	Spectral triples and Gibbs measures for expanding maps on Cantor sets	2012	Richard Sharp
+	Distribution of ergodic sums for hyperbolic maps	2011	Mark Pollicott Richard Sharp
+	Statistics of matrix products in hyperbolic geometry	2011	Richard Sharp M Policott SergiÇ Kolyada Yuri I. Manin Manfred Möller P Moree Thomas Ward
+	On the Hannay–Ozorio De Almeida Sum Formula	2011	Mark Pollicott Richard Sharp
+	Spectral triples and Gibbs measures for expanding maps on Cantor sets	2010	Richard Sharp
+ PDF Chat	Pairs of periodic orbits with fixed homology difference	2010	Morten S. Risager Richard Sharp
+	Degeneracy in the length spectrum for metric graphs	2010	Richard Sharp
+	Comparing length functions on free group	2010	Richard Sharp
+	Statistics of matrix products in hyperbolic geometry	2010	Mark Pollicott Richard Sharp
+ PDF Chat	Distortion and entropy for automorphisms of free groups	2009	Richard Sharp
+	Large deviations for intermittent maps	2009	Mark Pollicott Richard Sharp
+	Large Deviations, Fluctuations and Shrinking Intervals	2009	Mark Pollicott Richard Sharp
+	Lengths, quasi-morphisms and statistics for free groups	2009	Matthew Horsham Richard Sharp
+ PDF Chat	The mathematical research of William Parry FRS	2008	Mark Pollicott Richard Sharp Selim Tuncel Dale R. Walters
+ PDF Chat	Addendum: An analogue of Artin reciprocity for closed orbits of skew products	2008	Mark Pollicott Richard Sharp
+	Periodic orbits and holonomy for hyperbolic flows	2008	Mark Pollicott Richard Sharp
+	Pairs of periodic orbits with fixed homology difference	2008	Morten S. Risager Richard Sharp
+	Chebotarev-type theorems in homology classes	2007	Mark Pollicott Richard Sharp
+	Pseudo-Anosov foliations on periodic surfaces	2007	Mark Pollicott Richard Sharp
+ PDF Chat	Critical exponents for groups of isometries	2007	Richard Sharp
+ PDF Chat	Directions and equidistribution in homology for periodic orbits	2007	DAVID COLLIER Richard Sharp
+	Correlations for pairs of closed geodesics	2005	Mark Pollicott Richard Sharp
+	Angular self-intersections for closed geodesics on surfaces	2005	Mark Pollicott Richard Sharp
+	Uniform estimates for closed geodesics and homology on finite area hyperbolic surfaces	2004	Richard Sharp
+	Livsic theorems, maximizing measures and the stable norm	2004	Mark Pollicott Richard Sharp
+	On Some Aspects of the Theory of Anosov Systems: With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows	2004	G. A. Margulis Richard Sharp
+	A local limit theorem for closed geodesics and homology	2004	Richard Sharp
+	Periodic Orbits of Hyperbolic Flows	2004	Richard Sharp
+	None	2002	Mark Pollicott Richard Sharp
+	Local limit theorems for free groups	2001	Richard Sharp
+	Closed Geodesics and Periods of Automorphic Forms	2001	Richard Sharp
+	Error terms for closed orbits of hyperbolic flows	2001	Mark Pollicott Richard Sharp
+ PDF Chat	Poincaré series and comparison theorems for variable negative curvature	2001	Mark Pollicott Richard Sharp
+	None	2001	Mark Pollicott Richard Sharp
+ PDF Chat	Linear actions of free groups	2001	Mark Pollicott Richard Sharp
+	Exponential error terms for growth functions on negatively curved surfaces	1998	Mark Pollicott Richard Sharp
+	Relative growth series in some hyperbolic groups	1998	Richard Sharp
+	The Manhattan curve and the correlation of length spectra on hyperbolic surfaces	1998	Richard Sharp
+	Large deviations for maps with indifferent fixed points	1998	Mark Pollicott Richard Sharp Michiko Yuri
+ PDF Chat	Comparison theorems and orbit counting in hyperbolic geometry	1998	Mark Pollicott Richard Sharp
+	Poincaré series and zeta functions for surface group actions on ℝ-trees	1997	Mark Pollicott Richard Sharp
+	Growth of periodic points and rotation vectors on surfaces	1997	Mark Pollicott Richard Sharp
+	The circle problem on surfaces of variable negative curvature	1997	Mark Pollicott Richard Sharp
+ PDF Chat	Large deviations and the distribution of pre-images of rational maps	1996	Mark Pollicott Richard Sharp
+ PDF Chat	Growth series for the commutator subgroup	1996	Mark Pollicott Richard Sharp
+	Periodic points and rotation vectors for torus diffeomorphisms	1995	Richard Sharp
+	Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature	1994	Mark Pollicott Richard Sharp
+	Rates of Recurrence for Z<sup> <i>q</i> </sup> and R<sup> <i>q</i> </sup> Extensions of Subshifts of Finite Type	1994	Mark Pollicott Richard Sharp
+	Closed orbits in homology classes for Anosov flows	1993	Richard Sharp
+ PDF Chat	The correlation of length spectra of two hyperbolic surfaces	1993	Richard Evan Schwartz Richard Sharp
+	Prime orbit theorems with multi-dimensional constraints for axiom a flows	1992	Richard Sharp
+	An analogue of Mertens' theorem for closed orbits of Axiom A flows	1991	Richard Sharp
+	Asymptotic formulae for closed orbits of hyperbolic flows	1990	Richard Sharp

Common Coauthors

Coauthor	Papers Together
Mark Pollicott	35
Rhiannon Dougall	6
Stephen Cantrell	4
George Kenison	4
Solly Coles	2
Anastasios Stylianou	2
Morten S. Risager	2
Thomas Ward	1
Selim Tuncel	1
P Moree	1
SergiÇ Kolyada	1
G. A. Margulis	1
Manfred Möller	1
Yuri I. Manin	1
M Policott	1
Michiko Yuri	1
Richard Evan Schwartz	1
Dale R. Walters	1
DAVID COLLIER	1
Matthew Horsham	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Zeta functions and the periodic orbit structure of hyperbolic dynamics	1990	William Parry Mark Pollicott	44
+	Symbolic Dynamics for Hyperbolic Flows	1973	Rufus Bowen	20
+ PDF Chat	Closed orbits in homology classes	1990	Atsushi Katsuda Toshikazu Sunada	17
+ PDF Chat	Distribution of periodic orbits of symbolic and Axiom A flows	1987	Steven P. Lalley	16
+	Closed orbits in homology classes for Anosov flows	1993	Richard Sharp	14
+ PDF Chat	Comparison theorems and orbit counting in hyperbolic geometry	1998	Mark Pollicott Richard Sharp	14
+	Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II	1961	Heinz Huber	13
+	Closed geodesics in homology classes on surfaces of variable negative curvature	1989	Steven P. Lalley	13
+	On Decay of Correlations in Anosov Flows	1998	Dmitry Dolgopyat	13
+	Exponential error terms for growth functions on negatively curved surfaces	1998	Mark Pollicott Richard Sharp	13
+	An Introduction to Ergodic Theory	1981	Peter Walters	12
+	Rates of Recurrence for Z<sup> <i>q</i> </sup> and R<sup> <i>q</i> </sup> Extensions of Subshifts of Finite Type	1994	Mark Pollicott Richard Sharp	12
+	Homology and Closed Geodesics in a Compact Riemann Surface	1988	Atsushi Katsuda Toshikazu Sunada	11
+	Homology and Closed Geodesics in a Compact Negatively Curved Surface	1991	Mark Pollicott	11
+	The combinatorial structure of cocompact discrete hyperbolic groups	1984	JamesW. Cannon	11
+ PDF Chat	Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits	1989	Steven P. Lalley	11
+ PDF Chat	The Chebotarov theorem for Galois coverings of Axiom A flows	1986	William Parry Mark Pollicott	11
+	Markov partitions for anosov flows onn-dimensional manifolds	1973	Marina Ratner	11
+	An Introduction to Ergodic Theory	1982	Peter Walters	10
+	Lalley's theorem on periodic orbits of hyperbolic flows	1998	Martine Babillot François Ledrappier	10
+	Sur les Groupes Hyperboliques d’après Mikhael Gromov	1990	Étienne Ghys Pierre de la Harpe	10
+	Thermodynamic Formalism	2004	David Ruelle	10
+	None	2001	Mark Pollicott Richard Sharp	10
+ PDF Chat	Perturbation Theory for Linear Operators	1995	Tosio Kato	10
+	Prime orbit theorems with multi-dimensional constraints for axiom a flows	1992	Richard Sharp	10
+ PDF Chat	Precise counting results for closed orbits of Anosov flows	2000	Nalini Anantharaman	10
+	Geodesics in homology classes	1987	Ralph S. Phillips Peter Sarnak	10
+ PDF Chat	Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms	1975	Rufus Bowen	10
+	Geodesic flows on closed Riemann manifolds with negative curvature	1969	D. V. Anosov	9
+ PDF Chat	Large deviations, averaging and periodic orbits of dynamical systems	1994	Yuri Kifer	9
+	A note on asymptotic expansions for closed geodesics in homology classes	2001	Motoko Kotani	9
+ PDF Chat	An extension of the theory of Fredholm determinants	1990	David Ruelle	9
+ PDF Chat	Geodesic flows, interval maps, and symbolic dynamics	1991	Roy L. Adler Leopold Flatto	9
+	The Ergodic Theory of Axiom A Flows	1975	Rufus Bowen David Ruelle	8
+ PDF Chat	Bowen's equidistribution theory and the Dirichlet density theorem	1984	William Parry	8
+	Prevalence of rapid mixing in hyperbolic flows	1998	Dmitry Dolgopyat	8
+ PDF Chat	Symbolic dynamics for geodesic floes	1981	Caroline Series	8
+	Axiom <i>A</i> Diffeomorphisms have Rational Zeta Functions	1971	Anthony Manning	8
+	The Equidistribution of Closed Geodesics	1972	Rufus Bowen	7
+	Geometrical Markov coding of geodesics on surfaces of constant negative curvature	1986	Caroline Series	7
+	An Analogue of the Prime Number Theorem for Closed Orbits of Axiom a Flows	1983	William Parry Mark Pollicott	7
+ PDF Chat	Mesures de Patterson-Sullivan sur le bord d’un espace hyperbolique au sens de Gromov	1993	Michel Coornaert	7
+	The ergodic theory of AxiomA flows	1975	Rufus Bowen David Ruelle	7
+	The weight-per-symbol polytope and scaffolds of invariants associated with Markov chains	1991	Brian Marcus Selim Tuncel	6
+	Density theorems for closed orbits	1988	Atsushi Katsuda	6
+	Entropy at a weight-per-symbol and embeddings of Markov chains	1990	Brian Marcus Selim Tuncel	6
+ PDF Chat	The correlation of length spectra of two hyperbolic surfaces	1993	Richard Evan Schwartz Richard Sharp	6
+ PDF Chat	Markov maps associated with fuchsian groups	1979	Rufus Bowen Caroline Series	6
+ PDF Chat	Large deviations in dynamical systems and stochastic processes	1990	Yuri Kifer	6
+	Zeta-functions for expanding maps and Anosov flows	1976	David Ruelle	6