On the injectivity of the X-ray transform for Anosov thermostats
Dan Jane, Gabriel P. Paternain · Discrete and Continuous Dynamical Systems · 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.