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pro vyhledávání: '"Sharp, Richard P."'
Autor:
Sharp, Richard
We give two short proofs of the abelian Livsi\v{c} theorem of Gogolev and Rodriguez Hertz. We show that these proofs may be extended to give new abelian Livsic theorems for positive density sets of null-homologous orbits and for amenable covers.
Externí odkaz:
http://arxiv.org/abs/2410.17104
Autor:
Everitt, James, Sharp, Richard
In this note we examine the proportion of periodic orbits of Anosov flows that lie in an infinite zero density subset of the first homology group. We show that on a logarithmic scale we get convergence to a discrete fractal dimension.
Comment: 8
Comment: 8
Externí odkaz:
http://arxiv.org/abs/2311.11970
Autor:
Dougall, Rhiannon, Sharp, Richard
We consider random walks on countable groups. A celebrated result of Kesten says that the spectral radius of a symmetric walk (whose support generates the group as a semigroup) is equal to one if and only if the group is amenable. We give an analogue
Externí odkaz:
http://arxiv.org/abs/2309.01766
Vocoders are models capable of transforming a low-dimensional spectral representation of an audio signal, typically the mel spectrogram, to a waveform. Modern speech generation pipelines use a vocoder as their final component. Recent vocoder models d
Externí odkaz:
http://arxiv.org/abs/2208.12782
Autor:
Coles, Solly, Sharp, Richard
Consider a transitive Anosov flow on a closed $3$-manifold. After removing a finite set of null-homologous periodic orbits, we study the distribution of the remaining periodic orbits in the homology of the knot complement.
Externí odkaz:
http://arxiv.org/abs/2207.13608
Autor:
Pollicott, Mark, Sharp, Richard
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 the wellknown classical Selberg zeta function and L-function for Fuchs
Externí odkaz:
http://arxiv.org/abs/2203.15741
Autor:
Coles, Solly, Sharp, Richard
This paper concerns connections between dynamical systems, knots and helicity of vector fields. For a divergence-free vector field on a closed $3$-manifold that generates an Anosov flow, we show that the helicity of the vector field may be recovered
Externí odkaz:
http://arxiv.org/abs/2109.02985
Autor:
Sharp, Richard, Stylianou, Anastasios
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 arguments from work of Dolgopyat, we consider varying and potentially shrin
Externí odkaz:
http://arxiv.org/abs/2010.15646
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