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A finite Livshits theorem and local length spectrum rigidity
Jonathan DeWitt, Spencer Durham, James Marshall Reber +1
We show that for closed negatively curved Riemannian manifolds whose length spectrum is exponentially separated, the length spectrum is a local isometry invariant. In particular, t…
Local smooth rigidity of Anosov diffeomorphisms in
James Marshall Reber, Sebastián Pavez-Molina
Given a conjugacy between two Anosov diffeomorphisms, the matching periodic data problem asks whether this conjugacy is smooth provided spectral data of the diffeomorphisms m…
Anosov magnetic flows on surfaces
James Marshall Reber, Yumin Shen
Using the quotient bundle introduced by Wojtkowski, we give necessary and sufficient conditions for a magnetic flow on a closed, oriented surface to be Anosov.
A positive proportion Livshits theorem
Caleb Dilsavor, James Marshall Reber
Given a transitive Anosov diffeomorphism or flow on a closed connected Riemannian manifold , the Livshits theorem states that a Hölder function is a coboun…