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

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  • 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.
    Mathematics Subject Classification: Primary: 37D40, 53C65; Secondary: 45P05.

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