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June  2009, 24(2): 471-487. doi: 10.3934/dcds.2009.24.471

On the injectivity of the X-ray transform for Anosov thermostats

Dan Jane 1, and  Gabriel P. Paternain 1,

1. 

Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge CB3 0WB, United Kingdom, United Kingdom

Received  July 2008 Revised  November 2008 Published  March 2009

We consider Anosov thermostats on a closed surface and the X-ray transform on functions which are up to degree two in the velocities. We show that the subspace where the X-ray transform fails to be s-injective is finite dimensional. Furthermore, if the surface is negatively curved and the thermostat is pure Gaussian (i.e. no magnetic field is present), then the X-ray transform is s-injective.
Keywords: generalised thermostat, X-ray transform, Pestov identity..
Mathematics Subject Classification: Primary: 37D40, 53C65; Secondary: 45P0.
Citation: Dan Jane, Gabriel P. Paternain. On the injectivity of the X-ray transform for Anosov thermostats. Discrete and Continuous Dynamical Systems, 2009, 24 (2) : 471-487. doi: 10.3934/dcds.2009.24.471
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