1 citations · 1 across the 5 of their papers we have counts for
12 papers
Distribution of periodic orbits in the homology group of a knot complement
Solly Coles, Richard Sharp
Consider a transitive Anosov flow on a closed -manifold. After removing a finite set of null-homologous periodic orbits, we study the distribution of the remaining periodic orbi…
Zeta functions in higher Teichmuller theory
Mark Pollicott, Richard Sharp
In this note we introduce zeta functions and L-functions for discrete and faithful representations of surface groups in PSL(d, R), for d >= 3. These are natural generalizations of…
Helicity, linking and the distribution of null-homologous periodic orbits for Anosov flows
Solly Coles, Richard Sharp
This paper concerns connections between dynamical systems, knots and helicity of vector fields. For a divergence-free vector field on a closed -manifold that generates an Anosov…
Statistics of multipliers for hyperbolic rational maps
Richard Sharp, Anastasios Stylianou
In this article, we consider a counting problem for orbits of hyperbolic rational maps on the Riemann sphere, where constraints are placed on the multipliers of orbits. Using argum…
Relative growth in hyperbolic groups
Stephen Cantrell, Richard Sharp
In this note we obtain estimates on the relative growth of normal subgroups of non-elementary hyperbolic groups, particularly those with free abelian quotient. As a corollary, we d…
Anosov flows, growth rates on covers and group extensions of subshifts
Rhiannon Dougall, Richard Sharp
The aim of this paper is to study growth properties of group extensions of hyperbolic dynamical systems, where we do not assume that the extension satisfies the symmetry conditions…