Richard Sharp

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math.DS2010

Spectral triples and Gibbs measures for expanding maps on Cantor sets

Richard Sharp

Let $T : Λ \to Λ$ be an expanding map on a Cantor set. For each suitably normalized Hölder continuous potential, we construct a spectral triple from which one may recover the associ…

math.DS2008

Pairs of periodic orbits with fixed homology difference

Morten S. Risager, Richard Sharp

We obtain an asymptotic formula for the number of pairs of closed orbits of a weak-mixing transitive Anosov flow whose homology classes have a fixed difference.